Scanning based spreads using a hedge ratio non-linear optimization model

ABSTRACT

The disclosed embodiments utilize hedge ratios to determine the optimal hedge ratio and associated scanning spread. This tells traders what ratios of the quantities of products they should have in their portfolio in order to maintain the status of the portfolios as delta neutral, i.e. be delta hedged, and receive optimal margin credits therefore.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional under 37 C.F.R. §1.53(b) of U.S. patentapplication Ser. No. 12/056,465 filed Mar. 27, 2008, now U.S. Pat. No.______, the entire disclosure of which is hereby incorporated byreference.

This application relates to and describes further aspects of theembodiments disclosed in the following patent applications, which areincorporated herein in their entirety by reference for all purposes:

-   -   U.S. patent application Ser. No. 11/030,815, titled “SYSTEM AND        METHOD FOR ACTIVITY BASED MARGINING”, (Attorney Ref. No.        4672/410), filed Jan. 7, 2005;    -   U.S. patent application Ser. No. 11/030,796, titled “SYSTEM AND        METHOD FOR EFFICIENTLY USING COLLATERAL FOR RISK OFFSET”,        (Attorney Ref. No. 4672/417), filed Jan. 7, 2005;    -   U.S. patent application Ser. No. 11/030,833, titled “SYSTEM AND        METHOD FOR ASYMMETRIC OFFSETS IN A RISK MANAGEMENT SYSTEM”,        (Attorney Ref. No. 4672/418), filed Jan. 7, 2005;    -   U.S. patent application Ser. No. 11/030,814, titled “SYSTEM AND        METHOD FOR DISPLAYING A COMBINED TRADING AND RISK MANAGEMENT GUI        DISPLAY”, (Attorney Ref. No. 4672/419), filed Jan. 7, 2005; U.S.        patent application Ser. No. 11/031,182, titled “SYSTEM AND        METHOD FOR FLEXIBLE SPREAD PARTICIPATION”, (Attorney Ref. No.        4672/420), filed Jan. 7, 2005;    -   U.S. patent application Ser. No. 11/030,869, titled “SYSTEM AND        METHOD FOR HYBRID SPREADING FOR RISK MANAGEMENT”, (Attorney Ref.        No. 4672/421), filed Jan. 7, 2005;    -   U.S. patent application Ser. No. 11/030,849, titled “SYSTEM AND        METHOD OF MARGINING FIXED PAYOFF PRODUCTS”, (Attorney Ref. No.        4672/507), filed Jan. 7, 2005;    -   U.S. patent application Ser. No. 11/845,198, titled “ASYMMETRIC        AND VOLATILITY MARGINING FOR RISK OFFSET”, (Attorney Ref. No.        4672/648), filed Aug. 27, 2007;    -   U.S. patent application Ser. No. 11/204,379, titled “SYSTEM AND        METHOD FOR USING DIVERSIFICATION SPREADING FOR RISK OFFSET”,        (Attorney Ref. No. 4672/587), filed Aug. 15, 2006; and    -   U.S. patent application Ser. No. 11/965,221, titled “MARGIN        OFFSETS ACROSS PORTFOLIOS”, (Attorney Ref. No. 4672/652), filed        Dec. 27, 2007.

COPYRIGHT NOTICE

A portion of the disclosure of this patent document contains materialwhich is subject to copyright protection. The copyright owner has noobjection to the facsimile reproduction by anyone of the patent documentor the patent disclosure, as it appears in the Patent and TrademarkOffice patent file or records, but otherwise reserves all copyrightrights whatsoever.

BACKGROUND

Futures Exchanges, referred to herein also as an “Exchange”, such as theChicago Mercantile Exchange Inc. (CME), provide a marketplace wherefuture contracts and options on futures are traded. In an example, afutures contract is a standardized, legally binding agreement to buy orsell a commodity, security, financial product or other underlyinginstrument or investment vehicle at a specified price at a predeterminedfuture time. The futures contract specifies commodity, quality,quantity, delivery date and settlement.

An option is the right, but not the obligation, to sell or buy anunderlying instrument (in this case, a futures contract) at a specifiedprice within a specified time. A put option on a future grants theright, but not the obligation, to sell a futures contract at the statedprice prior to the expiration date and a call option gives the buyer theright, but not the obligation, to purchase a specific futures contractat a fixed price (strike price) within a specified period of time. Thebuyer has the right to buy the commodity (underlying futures contract)or enter a long position (e.g., a position in which the trader hasbought a futures contract that does not offset a previously establishedshort position). A call writer (seller) has the obligation to sell thecommodity (or enter a short position (e.g., the opposite of a longposition) at a fixed price (strike price) during a certain fixed time.The term “short” refers to one who has sold a futures contract toestablish a market position, and who has not yet closed out thisposition through an offsetting procedure. An offset may refer to takinga second futures or options on futures position opposite to the initialor opening position (e.g., selling if one has bought, or buying if onehas sold).

The Exchange may act as a “clearing house” whereby trades are confirmed,matched and settled each day until offset or delivered. The clearinghouse may settle trading accounts, clear trades, collect and maintainperformance bond funds, regulate delivery and report trading data. TheClearing House acts as a central counterparty by which the clearinghouse is the buyer to each seller, and seller to each buyer, therebyprotecting buyers and sellers from financial loss by assuringperformance. An example of a clearing house is the Clearing House of theChicago Mercantile Exchange (“CME”). Although the disclosed embodimentsare described in reference to the CME, it all present and futureembodiments are applicable to any Exchange and/or clearing house,including those which trade in equities and other securities.

The Clearing House establishes clearing level performance bonds for andestablishes minimum performance bond requirements. A performance bond,also referred to as a margin, is the amount of funds that must bedeposited by a trader with his or her broker, by a broker with aclearing member or by a clearing member with the Clearing House, toinsure the broker or Clearing House against loss on open futures oroptions contracts. This performance bond is not a partial payment;rather, it acts to ensure the financial integrity of brokers, clearingmembers and the Exchange. The Performance Bond to Clearing House refersto the minimum dollar deposit which is required by the Clearing Housefrom clearing members in accordance with their positions. Maintenance,or maintenance margin, refers to a sum, usually smaller than the initialperformance bond, which must remain in the customer's account for anyposition at all times. The initial margin is the total amount of marginper contract required when a futures position is opened. A drop in fundsbelow this level requires a deposit back to the initial margin levels.If a customer's equity in any futures position drops to or under themaintenance level because of adverse price action, the broker must issuea performance bond/margin call to restore the customer's equity. Aperformance bond call, also referred to as a margin call, is a demandfor additional funds to bring the customer's account back up to theinitial performance bond level whenever adverse price movements causethe account to go below the maintenance.

CME derives its financial stability in large part by removing debtobligations among market participants. This is accomplished bydetermining a settlement price at the close of the market each day foreach contract and marking all open positions to that price, referred toas “mark to market.” Every contract is debited or credited based on thattrading session's gains or losses. As prices move for or against aposition, funds flow into and out of the trading account. Debtobligations from option contracts are also immediately removed, sincethe purchaser of an option must pay the premium (cost of the option) infull at the time of purchase. Sellers of options post performance bonds,discussed above, as determined by the CME according to the prevailingrisk characteristics of the options sold. CME's mark-to-the-marketsystem does not allow losses to accumulate over time or allow a marketparticipant the opportunity to defer losses associated with marketpositions.

If a clearing member does not have sufficient performance bondcollateral on deposit with the Clearing House, then the clearing membermust meet a call for cash performance bond deposits. Clearing members'performance bond deposits may only be:

-   -   Cash (such as U.S. dollars, Canadian and Australian dollars,        Japanese yen, Euro currency, Swiss francs, British pounds,        Norwegian krone, and Swedish krona);    -   U.S. Treasury securities;    -   Letters of credit issued in the Exchange's name by approved        banks;    -   Stocks selected from among approximately half of those in the        S&P's 500® Stock Price Index and depository trust shares based        on the S&P's 500 Stock Price Index;    -   Selected sovereign debt of Canada, France, Germany, and the UK;    -   Discount notes issued by the Federal Farm Credit Banks, Federal        Home Loan Mortgage Corporation, Federal Home Loan Bank System,        or Fannie Mae, provided that the notes have less than six months        remaining to maturity;    -   Fixed rate note and bond securities issued by the Federal Farm        Credit Bank, Federal Home Loan Bank, Federal Home Loan Mortgage        Corporation, Fannie Mae or Ginnie Mae;    -   Interest Earning Facility (IEF), a CME managed fund program;    -   IEF2: Money Market Mutual Funds allowable under CFTC Regulation        1.25; and    -   IEF3 and IEF4: Clearing firm self-directed collateral management        program.

The Clearing House Division monitors intra-day price movementsthroughout the trading session. To assess the impact of these pricechanges, an intra-day mark-to-the-market calculation may be performedand reviewed by the Clearing House and Risk Management Departmentsseveral times each day, more frequently if price volatility is high.Stress testing of clearing member positions may also be performed on adaily basis. Numerous stress scenarios have been modeled to reflect adiverse universe of possible market events. Stress results are evaluatedagainst performance bond on deposit and also with clearing memberadjusted net capital. Results of stress tests may lead to requests thatthe clearing member provide additional information about its customeraccounts such as whether there are non-CME offsetting positions in othermarkets. In some cases stress test results may cause increases to aclearing member's performance bond requirement, or reduce or transferpositions.

In order to minimize risk to the Exchange while minimizing the burden onmembers, it is desirable to approximate the requisite performance bondor margin requirement as closely as possible to the actual positions atany given time. Accuracy and flexibility of the mechanisms whichestimate performance bond requirements is therefore preferred.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an exemplary portfolio optimization system according toone embodiment.

FIG. 2 depicts a more detailed block diagram of the exemplary system ofFIG. 1.

FIG. 3 depicts flow chart showing exemplary operation of the portfoliooptimization system of FIG. 1.

FIGS. 4A to 4B depict exemplary performance bond requirements.

FIGS. 5-8 depict an operation of the system of FIG. 1 on an exemplaryportfolio.

DETAILED DESCRIPTION

By way of introduction, the disclosed embodiments relate to a systemand/or method for optimizing margin credits for portfolios whilemaintaining the delta neutral status of the portfolio. In particular,the disclosed embodiments utilize hedge ratios to determine optimalquantities of a given product to hold to maintain the delta neutralstatus of the portfolio while maximizing credit towards to marginrequirement therefore. As will be described in more detail below, thedisclosed embodiments tests quantity variations, which are based on thedelta neutral hedge ratios, in the various positions held against themargin credits offered for those positions to determine the variation ofquantities which results in margin credits which most closelyapproximate the maximum possible margin credit.

CME establishes minimum initial and maintenance performance bond levelsfor all products traded through its facilities. CME bases theserequirements on historical price volatilities, current and anticipatedmarket conditions, and other relevant information. Performance bondlevels vary by product and are adjusted to reflect changes in pricevolatility and other factors. Both initial and maintenance performancebonds are good faith deposits to guarantee performance on futures andoptions contracts. Maintenance performance bond levels represent theminimum amount of protection against potential losses at which theExchange will allow a clearing member to carry a position or portfolio.Should performance bonds on deposit at the customer level fall below themaintenance level, Exchange rules require that the account bere-margined at the required higher initial performance bond level.Clearing members may impose more stringent performance bond requirementsthan the minimums set by the Exchanges. At the Clearing House level,clearing members must post at least the maintenance performance bondsfor all positions carried. This requirement applies to positions ofindividual members, nonmember customers and the clearing member itself.

To set performance bond levels, the Clearing House monitors current andhistorical price movements covering short-, intermediate- andlonger-term data using statistical and parametric and non-parametricanalysis. Futures maintenance performance bond levels are set to coverat least the maximum one-day price move on 95% of the days during thesetime periods. The actual performance bond requirements often exceed thislevel.

Performance bond requirements for options reflect movements in theunderlying futures price, volatility, time to expiration and other riskfactors, and adjust automatically each day to reflect the unique andchanging risk characteristics of each option series. Long options mustbe paid for in full, and stringent minimum performance bonds aremandated for short option positions. Exemplary performance bondrequirements are shown in FIGS. 4A-4B.

The performance bonds may be calculated using a system developed andimplemented by CME referred to as Standard Portfolio Analysis of Risk™(SPAN®). Performance bond requirements are based on the overall risk ofthe portfolios. SPAN simulates effects of changing market conditions anduses standard options pricing models to determine a portfolio's overallrisk.

Futures and options may be treated uniformly while recognizing theunique features of options. In standard options pricing models, threefactors most strongly affect options values: the underlying futuresprice, volatility (variability of futures price) and time to expiration.As these factors change, futures and options may gain or lose value.SPAN constructs scenarios of futures prices and volatility changes tosimulate what the portfolio might reasonably lose over a one day timehorizon. The resulting SPAN performance bond requirement covers thispotential loss. SPAN evaluates overall portfolio risk by calculating theworst probable loss that a portfolio might reasonably incur over aspecified time period. This number is achieved by comparing hypotheticalgains and losses that a portfolio would sustain under different marketconditions. A ‘Risk Array” analysis of 16 possible scenarios for aspecific portfolio under various conditions is conducted. Users mayrequest any number of scenarios to meet their particular needs:

-   -   Each scenario consists of a “what-if” situation in which SPAN        assesses the effects of variations in price, volatility and time        to expiration; and    -   Each calculation represents a gain or loss based on the possible        gains or losses due to changes in an instrument's price by X and        volatility by Y. SPAN licensed clearing organizations and        exchanges may determine the following SPAN parameters, in order        to reflect the risk coverage desired in a market:    -   Price Scan Range: A set range of potential price changes;    -   Volatility Scan Range: A set range of potential implied        volatility changes;    -   Intra commodity Spread Charge: An amount that accounts for risk        (basis risk) of calendar spreads or different expirations of the        same product, which may not be perfectly correlated;    -   Short Option Minimum: Minimum margin requirement for short        option positions;    -   Spot Charge: A charge that covers the increased risk of        positions in deliverable instruments near expiration; and    -   Intercommodity Spread Credit: Margin credit for offsetting        positions between correlated products. SPAN combines financial        instruments within the same underlying for analysis, and refers        to this grouping as the Combined Commodity group. For example,        futures, options on futures and options on equities on the same        stock could all be grouped under a single Combined Commodity.

To calculate a performance bond requirement, for each Combined Commodityin a portfolio, SPAN:

-   -   Sums Scan Risk charges, any Intracommodity Spread and Spot        Charges;    -   Applies offsets for all Intercommodity Spread Credits within the        portfolio;    -   Compares the sum with existing Short Option Minimum        requirements; and    -   Assesses the greater of the two compared as the risk of the        Combined Commodity.

The Total Margin Requirement for a portfolio is the sum of the risk ofall Combined Commodities less all credit for risk offsets between thedifferent Combined Commodities.

As described, SPAN is utilized by Exchanges and clearing members andother entities as a tool that to determine anticipated performance bondrequirements of the clearing house which facilitates financial planningand certainty. It will be appreciated that the disclosed embodiments areequally applicable to both the version of SPAN used by the exchange andthe version used by the market participants and that any discussionherein referring to SPAN is intended to be applicable to bothapplications.

Another system for portfolio risk assessment is referred to as theTheoretical Intermarket Margin System (“TIMS”), by The Options ClearingCorporation, in Chicago, Ill. With TIMS, clearing institutions canmeasure, monitor and manage a level of risk exposure of their members'portfolios. TIMS can calculate risk exposure at different account levelsand for different account types. TIMS uses portfolio theory to marginall positions relating to the same underlying product and combines therisk of closely related products into integrated portfolios. Thisportfolio aspect of TIMS allows for the recognition of hedges used bymarket participants in increasingly interrelated markets. TIMS measuresthe monetary risk inherent in portfolios containing options, futures andoptions on futures positions. In particular, TIMS uses pricing models toproject the liquidation value of each portfolio given changes in theprice of each underlying product. These models generate a set oftheoretical values based on various factors including current prices,historical prices and market volatility. Based on flexible criteriaestablished by a clearinghouse, statistically significant hedges receiveappropriate margin offsets. TIMS also predicts a member's potentialintra-day risk under varying sets of assumptions regarding marketbehavior.

TIMS organizes all classes of options and futures relating to the sameunderlying asset into class groups and all class groups whose underlyingassets exhibit close price correlation into product groups. The dailymargin requirement for a clearing member is calculated based on itsentire position within a class group and various product groups. Themargin requirement consists of two components, a mark-to-marketcomponent and an additional margin component.

The mark-to-market component includes a premium margin calculation thatprovides margin debits or requirements for net short positions andmargin credits for net long positions. The margin debits and credits arenetted to determine the total premium margin requirement or credit foreach class group. The premium margin component represents the cost toliquidate the portfolio at current prices by selling the net longpositions and buying back the net short positions.

The additional margin component, the portion of the margin requirementthat covers market risk, is calculated using price theory in conjunctionwith class group margin intervals. TIMS projects the theoretical cost ofliquidating a portfolio of positions in the event of an assumed worstcase change in the price of the underlying asset. Theoretical values areused to determine what a position will be worth when the underlyingasset value changes. Given a set of input parameters (e.g., optioncontract specifics, interest rates, dividends and volatility), thepricing model will predict what the position should theoretically beworth at a specified price for the underlying instrument.

Another risk management system, referred to as OMS II, the “Windowmethod” or the “Vector method,” calculates worst case loss scenarios,store these in vectors, adjust for spreading, and adds the vectors in away that takes correlation in to account. In OMS II the valuationinterval is divided into n (normally n=31) possible up or down moves,additionally for each up or down move the volatility can either increasestand still or decrease. This provides 93 alternative market scenarios(if n=31) to calculate the profit or loss a portfolio will make. OMS IImay be viewed mathematically as producing the maximum of the expectedloss under each of 93 probability measures. For all 93 scenarios theprobability measures are point masses at each of the 93 points in aspace Ω of securities prices and volatilities. Each valuation point issaved in a 31×3 matrix, that is, each row contains a price move and thethree volatility fluctuations. The matrix is expanded to a 31×6 matrixso that the case of both a bought and a sold contract is represented inthe matrix, this because of additional fine-tunings that are availablein OMS II. The matrixes are saved for use when margin requirements ofportfolios are calculated.

For accounts containing positions of two or more types of contracts, theoverall risk is the combined risk characteristics for the differentcontracts registered to the account. Cross-margining may take theoffsetting characteristics of the instrument into account. Defaultcross-margining divides the positions into one group per underlying.Positions on instruments within the same underlying are correlated. Thedefault cross-margin may be considered instruments with the sameunderlying being totally correlated and instruments with differentunderlying being uncorrelated. During a default cross-margin run aportfolio with instruments on the same underlying will add the valuationfiles pointwise as in SPAN, and then take the largest negative value asthe margin requirement for the portfolio. If the portfolio includesinstruments on different underlyings, the largest negative value of eachvaluation file is added.

However, a default cross-margining method may not consider correlationsbetween different underlyings or different expiry months. Therefore, inOMS II, the “Window method” may be used when a portfolio containinginstruments on different underlyings or contracts with different expirymonths is margined. In the window method, the different instruments aresorted into a number of groups, called window classes. The windowclasses have a window size defined in percentage. When the percentagegoes down, the correlation goes up and vice versa (e.g., a window sizeof 0% means that the instruments are totally correlated, and a windowsize of 100% means that the instruments are uncorrelated). A windowclass may also be a member of another window class and create a treestructure of more complex correlations.

To calculate the margin for a portfolio, the window is moved from leftto the right over the entire valuation interval for all window classes,starting with the bottom of the tree. The window is centered over eachvaluation point. A margin requirement is calculated at each valuationpoint where the window is positioned by adding the lowest value for eachoption position or futures position in the window. The total marginrequirement will be the largest negative value of the marginrequirements. No negative values indicate a credit, and no margin isrequired.

A comparison of SPAN, TIMS and OMS II may be found in Bylund, Mattias,“A Comparison of Margin Calculation Methods for Exchange TradedContracts” (Feb. 21, 2002). Royal Institute of Technology Dept. ofMathematical Statistics, Master Thesis No. 2002-3.http://ssrn.com/abstract=300499, herein incorporated by reference. Whilethe disclosed embodiments will be discussed with reference to the SPAN®risk analysis software, it will be appreciated that they may also beapplicable to the TIMS risk analysis software, as well as other productsdirected at determining performance bond requirements and/or assessingrisk in a portfolio of derivatives.

The CME Clearing House requires “gross” performance bonds for customerpositions in CME products. A clearing member must deposit performancebonds for each open position (long or short) held at the end of tradingday, with appropriate allowances for spreads. A spread is the pricedifference between two contracts (e.g., holding a long and a shortposition in two related futures or options on futures contract) with theobjective of profiting from a changing price relationship or theassumption of a long and short position on the same business day in thesame or related commodities for the same account. A Spread order may bean order that indicates the purchase and sale of futures contractssimultaneously. An example of a spread trade includes the simultaneouspurchase and sale of futures contracts for the same commodity orinstrument for delivery in different months or in different but relatedmarkets. Other types of spread trading involve the simultaneous purchaseof one commodity contract against the sale of another related contract.A spread transaction may be established with an expectation that thedifferential between contacts will widen or narrow. If the trader buysthe higher, more valuable leg of the spread, he anticipates that thedifferential will widen. Conversely, if he sells the higher leg, hebelieves it will narrow. Natural spreads are available, for example, inthe energy market between different months of the same commoditycontract, as well as between different products and grades. There arefour basic types of spreads:

-   -   Intramarket Spreads: a long position in one contract month        against a short position in another contract month in the same        commodity.    -   Intermarket Spread: Similar or related commodities on different        exchanges.    -   Intercommodity Spreads: A long position in one commodity, and a        short position in a different but economically related        commodity.    -   Commodity-Product Spreads: The purchase of a commodity against        the sale of an equivalent amount of the product derived from it        (or vice versa). In the oil market, this is referred to as a        “crack spread.”

Calculating Risk Performance Bond/Margin Requirements

The SPAN system is applicable to an unlimited range of product types.Portfolios today, however, can contain the widest range of derivativeand non-derivative instruments. SPAN supports and provides for productflexibility using an advanced, object-oriented model. In particular,current implementations adds support for equity and debt securities(stocks, bonds, etc.), and options thereon, foreign exchange, andoptions thereon.

Account types: Portfolios of positions to be margined are held inperformance bond accounts, or margin accounts. The positions in anaccount constitute a single portfolio. If this is a particularperformance bond account of a clearing member firm at a clearingorganization, we say that the risk analysis done by that clearingorganization for that account is a clearing-level calculation. On theother hand, risk analysis calculations may be performed for particularcustomer or other accounts of firms which are clearing members, directlyor indirectly, of one or more clearing organizations. These arefirm-level, also called customer-level, calculations.

For any performance bond account, the account type is defined by:

(a) whether the account is a clearing-level account or a firm-levelaccount, and(b) the specific account type code, for example, member, hedger, orspeculator.

Business Functions and Exchange Complexes

A business function represents a particular purpose for which anexchange or clearing organization wishes to perform the risk analysiscalculation or have it performed, at either the clearing-level or thecustomer-level. For example:

-   -   Normal clearing-level calculations for the particular clearing        organization may be utilized to analyze normal clearing-level        account types;    -   Special member-clearing calculations may be utilized to analyze        member clearing account types;    -   Normal customer-level calculations may be utilized for the part        of a portfolio traded on, or cleared by, a particular exchange        or clearing organization    -   Clearing-level calculations may be utilized for a particular        cross-margin agreement between clearing organizations    -   Customer-level calculations may be utilized for a customer        portfolio associated with a particular cross-margin agreement

By definition, a clearing-level calculation for a portfolio is alwaysfor a specific business function. That is, the portfolio is identifiedwith a specific business function, and may contain only productseligible for that business function. By contrast, a customer-levelportfolio may have any number of business functions represented withinthe portfolio. Business functions are also referred to as exchangecomplexes, and the identifier for a business function as the exchangecomplex acronym.

Requirement Levels:

For particular business functions, the exchange or clearing organizationmay mandate the calculation of more than one requirement number. Eachnumber is called a requirement level, and is specific to: (a) theperformance bond class of the requirement level, and (b) the initial ormaintenance designation of the requirement level.

Performance bond classes may designate different levels of requirements.The first class (the one with the lowest requirement level) is speciallydesignated as the core class and the second class (the one with thenext-highest requirement level) as the reserve class. Any number ofperformance bond classes can be defined, and for any purpose. The mostcommon purpose is to recognize different requirement levels that may bemet by different classes of collateral assets. Typically the corerequirement must be met by the highest-quality assets. The differencebetween the core requirement and the higher reserve requirement, e.g.,the reserve additional requirement, may be met by certain lesser-qualityassets. Within the specific performance bond class, the exchange orclearing organization may mandate the distinction between the initialrequirement level and the maintenance requirement level.

Combined Commodities

For each business function for which an exchange or clearingorganization is using SPAN, the set of products eligible for thatbusiness function may be grouped into combined commodities. For eachbusiness function and for each combined commodity represented withinthat business function, SPAN yields one or more SPAN risk requirements.Each such requirement corresponds to a specific SPAN requirement level—aspecific performance bond class and an initial or maintenancedesignation. SPAN requirements calculated for individual combinedcommodities represented in the portfolio are then aggregated to yieldSPAN requirements for the different business functions representedwithin the portfolio, and for the entire portfolio. The combinedcommodity may be thought of as the atomic-level of the SPAN calculation.It is the lowest breakdown of the products within a portfolio at which aperformance bond requirement is obtained. Typically, all products on thesame ultimate underlying physical are grouped together into a combinedcommodity.

Performance Bond Currencies

For each combined commodity, a single currency is specified as theperformance bond currency for that combined commodity. This is thecurrency in which the performance bond requirement for a combinedcommodity represented within a portfolio, will be denominated. Anynumber of performance bond currencies may be represented within theportfolio. Therefore, when aggregating requirements for the differentcombined commodities represented within the portfolio, these aretypically first aggregated by performance bond currency. Thesecurrency-level requirements may then be converted to a common currencyfor further aggregation. This common currency may be the native currencyfor the portfolio.

Span Risk Parameter Files

Clearing organizations and/or exchanges publish, at least once daily,one or more SPAN risk parameter files. SPAN risk parameters may begenerically defined as the set of data needed to calculate SPANrequirements, other than the actual portfolios for which therequirements are to be calculated. SPAN risk parameters include (a)product data and (b) performance bond rate data. Typically, SPAN riskparameter files include data for exactly one point in time, and ineffect, include data used for performance bond calculations forportfolios existing at that point. Within each point in time, the SPANfile includes data for one or more business functions of the exchange orclearing organization publishing the file. Within each businessfunction, the file will contain data for each combined commodity for thebusiness function. Ultimately, the file will contain many different SPANrates—for example, risk arrays, intracommodity spread charge rates,intercommodity spread credit rates, etc. Each such rate is qualified bythe account type and requirement level to which it pertains.

Point in Time

Risk parameters and portfolios are defined at particular points in time.Points in time are categorized as to whether they are for an end of daysettlement, or an intraday point in time. Some clearing organizations,for some business functions, may publish more than one SPAN file for theend-of-day settlement. These are typically distinguished as being for:(a) the final settlement; (b) an early (or preliminary) settlement; or(c) the complete settlement.

In the early settlement SPAN file, typically final end-of-day settlementprices are available only for some of the products, while other productshave intraday prices provided. The final settlement file typicallycontains final settlement prices for the day for all actively tradingcontracts. The complete file will contain final settlement prices forall contracts, actively trading or inactive.

An intraday point in time is further characterized by its businesstime—indicating the actual time to which prices and risk arrays pertain.A point in time, whether intraday or end of day, may also becharacterized by its run number—for example, the first intraday run, thesecond intraday run, etc.

Risk Arrays, Risk Scenarios, Composite Deltas, Scan Points And DeltaPoints Risk Arrays

A risk array is a set of numbers defined (a) for a particular contract,(b) at a particular point in time, (c) to be margined for a particularbusiness function, (d) associated with a particular account type, and(e) a particular requirement level, performance bond class and initialor maintenance designation, associated with that account type of item(d).

Each risk array value specifies how a single long or short position willlose or gain value if the corresponding risk scenario occurs over thespecified look-ahead time. By convention, losses for long positions areexpressed as positive numbers, and gains as negative numbers.

Lookahead Time

The lookahead time reflects the amount of time in the future from thecurrent time, for which the SPAN requirement levels are intended toprotect against declines in portfolio value. Lookahead time is aparameter of SPAN and may be set to any desired value. There may be twomethods which can be utilized to determine or calculate the lookaheadtime, these methods are discussed below.

Actual Time to the Next Business Day

The Actual time to the next business day method determines the number ofcalendar days from the current business day to the next business day.The difference between these twp date may then be divided by 365 daysper year to determine the lookahead time in years.

Average Time Per Business Day

The average time per business day method determines the lookahead timeas one business day in a business year. The business year may be assumedto have 250 business days per year, or 0.004 years.

Use of actual time to the next business day closely protects against therisk of larger changes in portfolio value over weekends and holidays,and may result in increased portfolio performance bond requirements onthe business day prior to a weekend, especially a holiday weekend. If,however, it is desired to avoid having the performance bond requirementfluctuate merely because of weekends and holidays, use of average timeper business day is more appropriate.

Risk Scenarios

A risk scenario may be defined based on, for example, the followingterms: (a) the (underlying) price movement, (b) the (underlying)volatility movement, and (c) the weight, also called the coveredfraction.

For futures, physicals and other non-option product types, these are theprice movement and volatility movement for the instrument itself. Foroptions, these are the price and volatility movements for the underlyinginstrument. The values of the price movement, the volatility movement,and the covered fraction are determined by the scan point definitionsand the two scan ranges, e.g., the price scan range and the volatilityscan range. These values are the key inputs to SPAN.

Scan Point Definitions:

Each scan point definition may consist of: (a) the price scan magnitude,as the number of price scan ranges up or down, for example, 0.3333 or−2.000 (meaning one third of the price scan range up, or twice the pricescan range down), (b) the volatility scan magnitude, as the number ofvolatility scan ranges up or down, for example, 1.0000 or −1.000(meaning the full volatility scan range up or down), (c) the weight.

The price scan magnitude may itself be expressed in terms of a pricescan numerator, a price scan denominator, and a price scan direction.For example, a price scan magnitude of −0.3333 may be expressed as anumerator of one, a denominator of three, and a direction of down.Similarly, the volatility scan magnitude may be expressed in terms of avolatility scan numerator, a volatility scan denominator, and avolatility scan direction.

Calculation of Risk Array Values:

Generally, each risk array value may be calculated as: (a) the currentvalue of the contract, (b) less the hypothetical future value of thecontract, after the look-ahead time has passed, and (underlying) priceand volatility movements associated with the risk scenario have occurred(d) multiplied by the weight.

For futures, physicals and certain types of combinations, this change invalue is determined by the price change alone. To determine thehypothetical future value for options, the underlying price change,underlying volatility change, decrease in time to expiration, and theassociated interest rates must also be taken into account, and atheoretical price calculated using an option pricing model.

In order to ensure that biases in the option pricing model do not affectthe result, the current value may also be calculated using the sameoption pricing model, assuming the current time to expiration, currentunderlying price, and current underlying volatility. In other words, therisk array value for an option is determined by subtracting thehypothetical future theoretical value of the option, from the currenttheoretical value of the option. The actual model selected, theparameters of the model, the interest rates, and the look-ahead time areall parameters of SPAN.

Composite Delta and Delta Point Definitions:

The composite delta value is associated with each risk array defined fora contract. The composite delta is a probability-weighted average of aset of deltas calculated for the contract (a) after the look-ahead timehas passed and (b) according to the scenarios defined by the definitionof the delta points. Delta points are defined exactly analogously toscan points, with a price scan magnitude, a volatility scan magnitude,and a weight. Suppose, for example, that there are seven delta pointsdefined. Seven delta values are calculated for the contract, using theprice scan magnitude and the volatility scan magnitude associated witheach delta point, and assuming that the look-ahead time has passed. Aweighted average of these deltas is then taken; using the weightsspecified in the delta point definitions. In effect, a composite deltavalue represents an estimate of what the contract's delta will be afterthe look-ahead time has passed.

Overall Span Process:

To calculate SPAN requirements for a particular portfolio defined at aparticular point in time, in which particular business functions forparticular exchanges or clearing organizations are represented, the SPANprocess: (1) obtains, loads or other wise utilizes the applicable SPANrisk parameter file(s), (2) utilizes the SPAN algorithm in conjunctionwith the positions in the portfolio and the data contained in the SPANrisk parameter files. The results of steps (1) and (2) yields therequirement(s): (a) for the specific account type, (b) for each combinedcommodity of each business function represented in the portfolio, and(c) for each combined commodity, for each applicable requirement level(performance bond class, initial or maintenance designation).

Determine (Direct and Indirect) Requirement Levels for a Portfolio

For a combined commodity in a portfolio of a particular account type, itis necessary to select the set of performance bond requirement levels(e.g., unique combinations of performance bond class and initial ormaintenance designation) for which SPAN requirements should becalculated, directly or indirectly. A directly calculated SPANrequirement is a requirement, at a particular performance bondrequirement level, for which the full SPAN calculation is done (e.g.,scanning, spreading, etc). An indirectly calculated requirement is onethat is derived from another requirement, at a different requirementlevel, by the application of a simple multiplicative scaling factor.Indirectly calculated requirements are also known as derivedrequirements. The selection of the set of requirement levels to bedirectly calculated, for a particular combined commodity in a portfolio,is driven by the set of requirement levels represented in the riskarrays for the products in that combined commodity. In particular, thisis driven by which set of requirement levels are present for whichaccount types. If there are risk arrays for this combined commodity forthe particular account type of the portfolio, then these are the onesthat determine the requirement levels to be directly calculated.

Risk Adjustment Factors and Derived Requirements

For each combined commodity, any number of risk adjustment factors maybe provided in the SPAN risk parameter file. Risk adjustment factors maybe used either to adjust requirements at directly calculated risklevels, or to derive requirements at other risk levels (indirectcalculation.) Each risk adjustment factor has the following defined forit: (a) the account type to which it pertains, (b) the base requirementlevel, e.g., the requirement level, performance bond class and initialor maintenance designation, which will be used to derive another one,(c) the target requirement level which may be adjusted or derived, and(d) the value of the factor.

To apply a risk adjustment factor, multiply the requirement at the baselevel by the value of the factor. Adjustment factors used to derive aninitial requirement for a particular performance bond class from amaintenance requirement for that class are also known as initial tomaintenance ratios.

Summarized Span Calculation

A directly-calculated SPAN requirement at a particular requirement levelfor a combined commodity in a portfolio is calculated as: (1) sum thescan risk, the intracommodity spread risk, and the delivery (spot) risk,(2) subtract the intercommodity spread credit, and (3) take the largerof this result, and the short option minimum.

Scan risk is considered the risk for a combined commodity in aportfolio, assuming perfect correlations in price and volatilitymovements of the underlying instruments over time.

The intracommodity spread risk allows the recognition of risk associatedwith spreading within the combined commodity for combined commoditieswhere there is imperfect correlation of price and volatility movementsover time, and allows precise targeting of these requirements toparticular intracommodity strategies.

The delivery, or spot risk, recognizes the unique risk characteristicsof physically deliverable products, and of derivatives based on suchphysically deliverable products, as they approach the delivery period orgo through the delivery process.

The intercommodity spread credit provides appropriate creditsrecognizing risk offsets between positions in the different combinedcommodities represented in the portfolio.

The short option minimum recognizes the unique characteristics of shortoption positions, and allows the recognition of a minimum risk value fordeep out-of-the-money short options.

The sum of the scan risk, intracommodity spread risk, and the deliveryrisk is often referred to as the commodity risk, e.g., it is the riskfor the combined commodity in the absence of any credits forintercommodity spreading.

The result obtained by subtracting the intercommodity spread credit fromthe commodity risk is often referred to as the pre-SPAN risk. This is adirectly calculated SPAN requirement, assuming that the short optionminimum requirement is less.

Clearing Organizations, Exchange Groupings, and Product Families

At the highest level, products are cleared by clearing organizations.Each clearing organization may have one or more exchange groupingsdefined for it. Within each exchange grouping, products are grouped intoproduct families. Generally, a product family is identified within anexchange grouping by a product code such as an alphanumeric value, and aproduct type such as futures, options on futures, etc. Each productfamily is also assigned a product family ID number that is unique withinthe clearing organization and may be unique within the exchangegrouping.

Product families may be defined in as specific a manner as desired. Forexample, other parameters used to make product families unique includethe settlement method (cash-settled or physically deliverable), thevaluation method (futures-style or equity-style), the settlementcurrency, and, for options, the exercise style (American or European).Contract size may also be used to define separate product families.

Contracts

In SPAN, tradable instruments, whether derivative or non-derivative, aregenerically referred to as contracts or as products. Contracts aregrouped together in product families, and product type is always one ofthe things that makes a product family unique.

Product Types and Underlying Product Types

Product types may be for physicals or derivatives and, if the latter,for combination or non-combination products. Each contract (product)which is not a physical of one or another type is classified as aderivative, and has one or more underlying contracts. Derivativeproducts that have exactly one underlying contract are known asnon-combination derivatives. Derivative contracts that have two or moreunderlying contracts are generically known as combinations. Each suchunderlying is referred to as a leg of the combination. Swaps, repos andreverse repos are recognized as subtypes of the combination type.

Contract Structure and Contract Underlying Ratios:

The set of underlying contracts for a derivative product is known as itscontract structure. Each element in the set specifies: (1) the specificunderlying contract; and (2) the underlying ratio for this specificunderlying contract. Underlying ratio may be defined for any contract Xwhich is not a physical: and for each of its underlying contracts Yi:

The underlying ratio is the number of units of that underlying Yi whichare bought (or sold) per one long position of the contract X, expressedas a positive number if buying, or a negative number if selling.

In other words, the underlying ratio informs: (1) whether buying thederivative means buying or selling this specific underlying contract;and (2) how many of the specific underlying are bought or sold perpurchase of one derivative contract.

Contract Price and Contract Value Calculations

Every contract, at every point in time, has a contract price associatedtherewith. For exchange-traded instruments, for SPAN being used as anend-of-day tool for calculating performance bond (margin) requirements,this will be the end-of-day settlement price. At other points in time(e.g., during the trading day) this may be an intraday theoreticalprice. SPAN uses the price of a contract to determine the monetary valueof a single position in that contract, e.g., the contract value. Thismonetary value is expressed in the settlement currency for the contract,also called the price quotation currency.

To calculate contract value multiply the contract price by the contractvalue factor for the contract. The contract value factor is themultiplier, which converts a quoted price for the contract into itsmonetary value in the contract's settlement currency. The contract valuefactor may be derived from the specification of the contract size andthe convention used for quoting prices.

Contract Periods

The concept of contract period denotes products with differentmaturities or expirations. Contract period can be thought of as ageneralization of the contract month concept. All contracts (exceptthose that are margined on an equivalent basis) have a contract periodcode defined. A contract period code may have, for example, thefollowing structure: (1) a four-digit year number, for example, 1999;(2) a two-digit month number, for example, 05 for May; and, if needed,(3) a two-byte string which may be used to further qualify the period.

Option Series

An option series in SPAN 4 consists of all options with the sameexpiration and the same underlying. Standard options within a seriesdiffer from each other only in their strike price and their option right(e.g., puts or calls). For more exotic options, they may also bedistinguished by one or more barrier prices.

Participation of product families in business functions: A productfamily is said to participate in a particular business function, if ithas been assigned to one of the combined commodities defined for thatbusiness function. Every product family always participates in thenormal clearing business function for its clearing organization. It may,but is not required to, participate in additional business functions.

Combined Commodities and Delta Periods

The products assigned to a combined commodity determine an array ofdelta periods defined for that combined commodity. Each contract ismapped into a specific delta period, and delta periods in turn aremapped into tiers.

Tiers and Tiered Processing

A tier in SPAN is a contiguous range of delta periods within a combinedcommodity. To provide flexibility, tiered processing is supported forscan rate tiers (the specification of tiers for defining price scanranges and volatility scan ranges), scanning tiers, intracommodityspread tiers, intercommodity spread tiers, and short option minimum ratetiers. Specific tiers for a combined commodity are identified by a tiernumber beginning with one, and are further qualified by a beginningperiod code and an ending period code. The ending period code must begreater than or equal to the beginning period code, and the deltaperiods for the different tiers never overlap.

For intra- and inter-commodity spreading, sometimes there are caseswhere more than one tier is defined, but it is desired in a particularleg of a spread to reference the entire combined commodity, across alltiers. To support this, SPAN recognizes for each combined commodity anintracommodity spread tier zero and an intercommodity spread tier zero,which are defined as the range of period codes for the entire combinedcommodity, crossing individual tiers. This may also be referred to asthe overall tier.

Mapping Each Delta Period into its Tier

For a given tier type for a combined commodity, to determine the tierinto which a delta period maps: (1) compare the delta period code withthe beginning period and the ending period, and (2) if the delta periodcode is greater than or equal to the beginning period, and less than orequal to the ending period, then it maps into that tier.

Portfolios to be Margined

As described above, a portfolio of positions to be margined using SPANis held in an account. Each such account has a specific account type.Portfolios may be defined at either the clearing-level or thecustomer-level. In other words, they are either for a specificperformance bond account of a clearing member firm of a clearingorganization, where the margin calculation is being done by thatclearing organization, or they are for a specific customer-level accountof a member firm or other trading firm, where the margin calculation isbeing done by that firm. A clearing-level portfolio always holdspositions for a single business function of that clearing organization,while any number of business functions and clearing organizations may berepresented in the positions for a customer-level portfolio.

Position Definition

A position within a portfolio to be margined at a particular point intime, is defined by: (a) the time at which the portfolio exists, (b) theportfolio in which the position is contained, specified as the firmidentifier, the account identifier, the account type (including whetherthis is a clearing-level or firm-level account), and the segregationtype, (c) the contract in which the position is held, and the businessfunction for which the contract is to be margined, and (d) the positionquantity number(s).

Gross and Net Position Management

A gross position is one that may be simultaneously long and short. A netposition is one that is never simultaneously long and short. In otherwords, a net position is one that is determined by netting together thebeginning position for the day with all buys and sells for that day. Fornet positions, all trades are liquidating to the extent possible. Agross position is determined by the beginning of day position and, foreach trade done for that day, whether it was an opening (new) or closing(liquidating) transaction. At the firm-level, accounts are commonly keptnet, with two typical exceptions: (1) omnibus accounts, discussed below,and (2) certain types of hedger accounts. At the clearing level,positions are typically kept gross for accounts which themselves areaggregates of more than one account at the firm level, in order toreflect true open interest.

Net Margining

At the firm-level and often at the clearing-level, portfolios aretypically “net margined.” This is also typically called “calculating anet requirement.” This means two things: (1) If the position is keptgross (e.g., if the position may be simultaneously long and short) thenit is first netted before being processed. Only the portfolio of netpositions is margined. And (2), no restrictions are placed on therecognition of risk offsets between different parts of the portfolio.

Since SPAN does recognize all allowable risk offsets, as they aredefined in the SPAN risk parameter file and as they are present in theportfolio, “net margining” translates into, process a portfolio of netpositions via SPAN. Note that there is a distinction between gross andnet position keeping, and gross and net margining: A position may besimultaneously kept gross, while being margined net. This is sometimesthe case for certain types of hedge customer accounts.

Omnibus accounts and levels of disclosure; gross margining at firmlevel: An omnibus account is an account of one firm on another firm'sbooks, which account is itself comprised of a number of individualaccounts on the first firm's books. The firm with the omnibus account issaid to carry the omnibus account on its books, and is often called the“carrying firm.” The individual accounts on the first firm's books aresaid to be “subaccounts” of the omnibus account. Because an omnibusaccount is comprised of any number of subaccounts, omnibus accountpositions must be kept gross. Any given position in any omnibus accountmay itself be the sum of a number of subaccount positions, some of whichmay be long and some of which may be short. If the omnibus account is“fully disclosed” to the carrying firm which must calculate a marginrequirement for it, this means that it has informed the carrying firm ofeach individual subaccount and what its positions are. Depending onbusiness practices, this may not mean that it has identified the ownerof each subaccount, but rather simply that it is has specified whichsets of positions belong to single owners. In this case, the carryingfirm typically calculates a net requirement for each subaccount, and thetotal omnibus account requirement is simply the sum of the subaccountrequirements. On the other hand, an omnibus account portfolio may beonly “partially disclosed”, or “non-disclosed.” If partially disclosed,the omnibus account has provided information to the carrying firm aboutsome sets of subaccounts, but not of all. If non-disclosed, noinformation is provided about the subaccounts and which positions theyhold.

The portion of each gross omnibus account position which is not held indisclosed subaccounts, is typically said to be “naked”. In other words,for each position—total long and total short—there is a nakedportion—the naked long and naked short. These naked positions aretypically “gross margined.” This means that (a) a separate SPANrequirement is calculated for each naked long position quantity, and foreach naked short position quantity. Because each such position quantityis in a single contract, and is only on one side of the market, thereare no risk offsets recognized in such requirements. And (b) that thetotal requirement for the naked portion of the account portfolio is thesum of all of these individual naked long and naked short requirements.

If the omnibus account is partially disclosed, its total requirement isthe sum of all of the net requirements for the subaccounts, plus the sumof all of the individual naked long and naked short requirements for thenaked positions.

Gross-Margining at the Clearing Level

At the clearing-level, the overall term “gross margining” is used torefer to a business practice where: (1) Positions are kept gross, e.g.may be simultaneously long and short; (2) Some portion of the total longand total short for each position is broken out, and margined net. Thisportion is termed the fully inter-commodity spreadable long and short,and is often referred to as the “intercommodity spreadable,” the“inter-spreadable” long and short, or the “inter positions”; (3) Anotherportion of each total position is broken out, and margined net, exceptthat no risk offsets are recognized among the different combinedcommodities in the portfolio, e.g., no intercommodity spreading is done.This portion is termed the “intracommodity spreadable”, the“intra-spreadable” or the “intra positions”; (4) The remaining portionis considered naked, and margined gross.

Some portion of the total positions may be deemed to be spreadable bothwithin commodities and between commodities, while another portion to bespreadable only within commodities but not between commodities, and afinal portion to be spreadable not at all. The total requirement foreach combined commodity in the clearing-level portfolio is thendetermined from the various components of the SPAN requirementscalculated for these different position types. So at the clearing-level,“gross margining” doesn't mean that positions are fully gross margined,but rather that some portion of the overall positions may be.

Clearing-level gross margining is typically used for customer-originperformance bond accounts where the clearing-level positions aredetermined by aggregating positions across many individual customeraccounts. Typically, the positions within each customer account areinspected to determine whether risk offsets exist both within andbetween commodities, or only within commodities, or not at all. Based onthis inspection, the customer's positions are classed asinter-spreadable, inter-spreadable, or naked. The total clearing-levelinter-spreadable long and short positions, then, are calculated as thesum of the customer positions that were classed as inter-spreadable, andanalogously for the intra-spreadable positions.

Position Accounts, Performance Bond Accounts, Margin Dispositions, andPositions to be Margined

At the clearing-level, it is possible for a distinction to be drawnbetween the position accounts in which positions are kept, and theperformance bond accounts in which they are margined. In this case,there may be a great deal of flexibility in how positions roll up fromposition accounts to performance bond accounts. For example, positionsin products eligible for participation in a particular cross-marginagreement may be routed to a performance bond account specifically forthat cross-margin business function, whereas positions in otherproducts, not eligible for this cross-margin agreement, are routed to aperformance bond account specified as being for the normal businessfunction. Even within a particular position, if that position iseligible for more than one business function, the position itself may bebroken down into any number of “positions to be margined”, or“dispositions”, each of which is designated for a particular performancebond account and hence to be margined via the SPAN parameters for aspecific business function.

Within each disposition, the position-to-be-margined may be marginedeither “gross” or net. If “gross”, each total position-to-be-margined isfurther broken down into an inter-spreadable long and short, anintra-spreadable long and short, and a naked long and short. If “gross”,as described above, the inter-spreadable positions are margined net, theintra-spreadable positions are margined net but without allowingintercommodity spreading, and the naked positions are truly marginedgross.

The Span Calculation for Net Portfolios

This section includes the description of the algorithm for calculationof a SPAN risk requirement for each combined commodity represented in aportfolio to be margined on a net basis (“net portfolio”). This may beeither a customer-level portfolio or a clearing-level portfolio.

Position Processing

Position processing in SPAN consists of processing each position withineach combined commodity represented in the portfolio, for the purposesof:

-   -   Scanning: scaling up the risk array(s) for the contract by the        position quantity, and incrementing the overall risk array(s) by        these scaled-up risk array(s)    -   Delta calculation: scaling up the SPAN composite delta(s) for        the contract by the position quantity, and incrementing the        overall position delta(s) for the associated delta period by        these scaled-up composite delta(s)    -   Short option minimum calculation: determining the effect of the        position on the quantity for determination of the short option        minimum charge (also called the minimum commodity charge).    -   Position value calculation: evaluating the current monetary        value of each position, and incrementing the overall current        monetary values for the combined commodity, broken out by        whether the position is long or short and by whether the        contract is valued futures-style or premium-style.

Position Types for the Position Value Calculations:

Products can be categorized by whether their valuation method isfutures-style or premium-style: (1) for futures-style products, there isa daily mark-to-market for open positions, and the resulting settlementvariation amounts are paid or collected daily. (2) For premium-styleproducts, the full trade price (premium) is paid or collected when theposition is opened.

Futures contracts, of course, are valued futures-style; the daily markto market and the daily payment or collection for settlement variation(sometimes called “variation margin”) is what distinguishes them from aforward contract. Option positions are typically valued premium-style,but some exchange-traded options are valued futures-style.

The significance of whether a position is valued premium-style is asfollows: If a position is valued premium style, and if the full value ofthe premium is considered to have been paid (or collected), then thecurrent value of the position is counted as a collateral asset (if long)or a liability (if short). For the positions in each combined commodityrepresented in the portfolio, then, it is necessary to determine thevalue of those positions broken out the following ways: (1) by whetherthe positions are valued futures-style or premium-style; (2) by whetherthe position quantities are long or short; (3) by whether the positionsare in options or are not in options.

In other words, for each combined commodity in the portfolio, we willhave determined:

-   -   value of long non-option positions in products valued        futures-style;    -   value of short non-option positions in products valued        futures-style;    -   value of long option positions in products valued futures-style;    -   value of short option positions in products valued        futures-style;    -   value of long non-option positions in products valued        premium-style;    -   value of short non-option positions in products valued        premium-style;    -   value of long option positions in products valued premium-style;        and    -   value of short option positions in products valued        premium-style.

Note that in some cases, the exchange or clearing organization usingSPAN may establish a business rule regarding the timing of therecognition of value for premium-style products.

Special position-processing features: In addition to regular positionprocessing, SPAN supports several special position-processing featureswhich provide additional power and flexibility: (1) split allocation istypically used for positions in combinations and/or options oncombinations where the underlying instruments of the combination are indifferent physical commodities, the position in the combination or theoption on the combination, is split out (allocated) into positions onthe underlying instruments of the combination. (2) Delta-SplitAllocation is typically used for positions in combinations and/oroptions on combinations where the underlying instruments of thecombinations are at different expirations within the same physicalcommodity, similar to regular split allocation, but differs in that onlythe delta from the position in the combination or the option on thecombination, is split out to the delta periods of the underlying legs.(3) Equivalent Positions is used when it is desired to margin a positionin one instrument, as one or more equivalent positions in otherinstruments.

Expression of Net Position Numbers

For positions in a net portfolio, position quantities are expressed assigned numbers, positive for a net long position, and negative for a netshort position. Depending on the types of instruments in the portfolioand the conventions used for expressing their positions, it is possiblefor position quantities to be fractional (e.g., not whole numbers).

Pre-Processing for Margining Debt Securities on an Equivalent Basis

For positions in physical debt securities, which are being margined onan equivalent basis, it may be necessary to perform specialpre-processing to express the position quantities properly, even beforethe transformation of the debt securities position into its equivalents.This section describes that pre-processing. For government debtsecurities to be margined on an equivalent basis, positions should beexpressed in units of thousands of par value currency units in thecurrency of denomination. Positions to be margined in such physical debtsecurities are those resulting from not-yet-settled trades. The actualposition in such securities can sometimes be broken out as the sumof: 1) the net position from open outright trades, and 2) the netposition from open repos (or reverse repos) in which the on-leg hassettled but the off-leg has not yet settled, with a net repo positionexpressed as a positive number and a net reverse repo position expressedas a negative number. Such repos are referred to as same-day repos whenthey are entered into (and margined), since on the day they are enteredinto, the on-leg settles, leaving only the unsettled off leg to bemargined.

Repo and reverse repo positions where neither leg has settled aretypically considered to be next-day repos. In other words, the repo isentered into today, with the on-leg beginning tomorrow. Since the on-legand the off-leg are both not-yet-settled, these obligations cancel eachother out. So these next-day repo or reverse repo positions are notincluded in the margin calculation.

Processing Split-Allocation Positions

After transforming any positions to be processed on an equivalent basisinto their equivalents, the next step in position processing is to dealwith any positions that are to be handled using the split allocationmethod. Split allocation is typically used for positions in options onfutures intercommodity spreads. The method is generically applicable,however, to any combination product or option on combination product.The specification of whether split allocation is to be performed is donefor a product family linked into a combined commodity. Not all productfamilies linked into a combined commodity need be processed using splitallocation. In general, however, for the algorithm to yield the desiredresults, split allocation should be specified for both the options onthe combination, and the combination itself. Typically both of theseproduct families will be placed into the same combined commodity.

Determining Position Quantities for Further Processing

With positions to be processed on an equivalent basis transformed intotheir equivalents, and positions to be processed via split allocation,allocated out to their underlyings, we're now ready to determine theposition quantities to be carried forward in SPAN.

The following applies to all position types except positions processedon an equivalent basis. (As explained above, such positions play noadditional role in the calculations once they have been transformed intotheir equivalents.) The algorithm will evaluate five different valuesfor each position: (1) the total position; (2) the marginable position;(3) the position for valuation; (4) the position for scanning and (5)the positions for the short option minimum calculation, the number ofshort calls and the number of short puts.

For each position in the portfolio, the total position is equal to thesum of the position in the contract itself, the equivalent position, andthe position resulting from split allocation. The marginable position isequal to the total position times the contract-scaling factor. Theposition for valuation is the sum of the position in the contract itselfand the rounded position resulting from equivalents. The position forscanning is determined as follows: (1) If the product family for thisposition is processed either normally or via delta-split-allocation,take the marginable position; and (2) If the product family for thisposition is processed via split allocation, take zero.

The positions for the minimum commodity charge are determined asfollows: if this position is not for an option, then the number of shortcalls and the number of short puts are both zero. But if this positionis for an option: If the marginable position is zero or positive, thenthe number of short calls and the number of short puts are both zero.But if the marginable position is negative: If the option is a call, thenumber of short calls is equal to the absolute value of the product ofthe marginable position and the delta-scaling factor. The number ofshort puts is zero. If the option is a put, the number of short puts isequal to the absolute value of the product of the marginable positionand the delta-scaling factor. The number of short calls is zero.

Determining The Position Value

For each combined commodity in the portfolio and for each position inthe portfolio: (1) take the position for valuation as determined above;(2) Multiply this result by the value of a single contract, yielding thevalue of the position in the settlement currency for the contract; (3)If the performance bond currency for the combined commodity in which theproduct is contained is different from the settlement currency of theproduct, convert the value from the settlement currency to theperformance bond currency, rounding as may be needed to the normalprecision of the performance bond currency. This yields the value of theposition in the performance bond currency for the combined commodity.

Determining the Liquidation Risk Position Value

The Liquidation Risk calculation is a method of determining the ScanRisk, which has been introduced in SPAN for the Paris Bourse (SBF.) Thiscalculation requires the determination of a special position valuecalled the Liquidation Risk Position Value. As can be seen, this differsfrom the regular position value in that (a) it includes any positionquantity resulting from split allocation, and (b) for positions in debtsecurities, it is adjusted for the duration of the security. For eachcombined commodity in the portfolio for which “liquidation risk” hasbeen specified as the method for determining the scan risk:

For each position for products linked into this combined commodity: (1)Take the position for scanning, as determined above; (2) If thisposition is in a debt security, multiply this value by the duration ofthat security, expressed in years. (3) Multiply this result by the valueof a single contract; (4) If the performance bond currency for thecombined commodity in which the product is contained is different fromthe settlement currency of the product, convert this value from thesettlement currency to the performance bond currency. (5) Round thisresult as specified. (The rounding convention used by SBF forliquidation risk position value is to round down, toward zero, to fivedecimal places.) The result is the liquidation risk position value.

Determining the Currency Conversion Rates for the Intercurrency RiskScanning Feature of the Scan Risk Calculation

Intercurrency risk scanning is an optional feature of the scan riskcalculation which may be applied in cases where there are products whosesettlement currency is different from the performance bond currency ofthe combined commodity into which they are linked. When a product familyis linked into a combined commodity, it may be specified thatintercurrency risk scanning is applicable. If intercurrency riskscanning is specified, then the risk array values for that productfamily linked into that combined commodity are denominated in thesettlement currency for that product family. For each such settlementcurrency and performance bond currency pair, it is necessary todetermine the exchange rate up and the exchange rate down: (1) For agiven settlement currency and performance bond currency pair, read theintercurrency scan rate up and the intercurrency scan rate down. (Theseare provided in the London format SPAN file on the currency conversionrate record for that currency pair.) Express these values as decimalfractions. If the settlement currency is equal to the performance bondcurrency, take zero for these values. (2) Take the exchange ratemultiplier, which converts a value in the settlement currency to one inthe performance bond currency. If the settlement currency is equal tothe performance bond currency, take one for this value. (3) Multiply theexchange rate by the value of one plus the intercurrency scan rate up,yielding the exchange rate up. (4) Multiply the exchange rate by thevalue of one minus the intercurrency scan rate down, yielding theexchange rate down.

Determining the Scaled-Up Risk Array(s) and Delta(s) for the Position:

For each combined commodity in the portfolio for which scanning is beingperformed normally (not using the “liquidation risk” scanning method):For each product family in this combined commodity and for each positionin this product family: (1) Take the position for scanning as determinedabove. (2) For each directly calculated requirement level for thisportfolio type and combined commodity: (i) Take the risk array for thisproduct as linked into this combined commodity and for this requirementlevel. (ii) Multiply each element in the risk array by the position forscanning, yielding the scaled-up risk array for the position. (iii) Ifthe intercurrency risk scanning feature is enabled for this productfamily: (a) Multiply each element in the scaled-up risk array by theexchange rate up for this settlement currency/performance bond currencypair, yielding the scaled-up converted-up risk array. (b) Multiply eachelement in the scaled-up risk array by the exchange rate down for thissettlement currency/performance bond currency pair, yielding thescaled-up converted-down risk array. (iv) To determine the positiondelta: (a) Take the composite delta for this product as linked into thiscombined commodity and for this requirement level. (b) Multiply theposition for scanning by the composite delta and then by thedelta-scaling factor.

Aggregation of position values to the combined commodity: For eachcombined commodity in the portfolio and for each position in thecombined commodity: (1) take the position value as calculated above; and(2) using the position value, increment one of eight value buckets forthe combined commodity determined according to whether: (a) The positionvalue is long (positive) or short (negative); (b) the position is for anoption or a non-option; (c) the position is valued futures-style orpremium-style.

Aggregation of Short Option Positions

For each combined commodity in the portfolio, for each position in thecombined commodity and for each short option minimum rate tier for thecombined commodity: (1) Increment the number of short calls for theoverall tier by the number of short calls for the position as calculatedabove; and (2) Increment the number of short puts for the overall tierby the number of short puts for the position as calculated above.

Determining the Number of Short Option Positions for a Tier

If the short option minimum charge method for the combined commodity isgross: (1) take the sum of the number of short calls for the tier andthe number of short puts for the tier; and (2) If the short optionminimum charge method for the combined commodity is maximum, take thelarger of the number of short calls for the tier and the number of shortputs for the tier.

Determining the Short Option Minimum Charge:

For each combined commodity in the portfolio, for each directlycalculated requirement level, and for each short option minimum ratetier: (1) determine the number of short option positions for the tier;(2) multiply by the short option minimum charge rate to yield the chargefor the tier; and (3) take the sum of the charges for the specifictiers, yielding the overall charge for the combined commodity.

Aggregation of scaled-up risk array values to the scanning tier(s) andthe intercommodity spread tier(s): For each combined commodity in theportfolio for which scanning is being performed normally (not using the“liquidation risk” scanning method), for each position in the combinedcommodity and for each directly calculated requirement level for theportfolio: (1) if intercurrency risk scanning is not enabled for theproduct family for this position in this combined commodity: (a)Increment each element in the overall scanning tier risk array, by thecorresponding element in the scaled-up risk array for the position. (b)If there are specific scanning tiers for the combined commodity, selectthe specific scanning tier in which this product is contained, andincrement each element in the risk array for the specific tier, by thecorresponding element in the scaled-up risk array for the position. (c)Increment each element in the overall intercommodity spread tier riskarray, by the corresponding element in the scaled-up risk array for theposition. (d) If there are specific intercommodity spread tiers for thecombined commodity, select the specific intercommodity spread tier inwhich this product is contained, and increment each element in the riskarray for the specific tier, by the corresponding element in thescaled-up risk array for the position. (2) But if intercurrency riskscanning is enabled for the product family for this position in thiscombined commodity: (a) Increment each element in the overall scanningtier exchange rate up risk array for this settlementcurrency/performance bond currency pair, by the corresponding element inthe scaled-up exchange rate up risk array for the position. (b)Increment each element in the overall scanning tier exchange rate downrisk array for this settlement currency/performance bond currency pair,by the corresponding element in the scaled-up exchange rate down riskarray for the position. (c) If there are specific scanning tiers for thecombined commodity, select the specific scanning tier in which thisproduct is contained, and: (i) Increment each element in the exchangerate up risk array for the specific tier for this settlementcurrency/performance bond currency pair, by the corresponding element inthe scaled-up exchange rate up risk array for the position. (ii)Increment each element in the exchange rate down risk array for thespecific tier for this settlement currency/performance bond currencypair, by the corresponding element in the scaled-up exchange rate downrisk array for the position. (d) Increment each element in the overallintercommodity spread tier exchange rate up risk array for thissettlement currency/performance bond currency pair, by the correspondingelement in the scaled-up exchange rate up risk array for the position.(e) Increment each element in the overall intercommodity spread tierexchange rate down risk array for this settlement currency/performancebond currency pair, by the corresponding element in the scaled-upexchange rate down risk array for the position. (f) If there arespecific intercommodity spread tiers for the combined commodity, selectthe specific intercommodity spread tier in which this product iscontained, and: (i) Increment each element in the exchange rate up riskarray for the specific tier for this settlement currency/performancebond currency pair, by the corresponding element in the scaled-upexchange rate up risk array for the position. (ii) Increment eachelement in the exchange rate down risk array for the specific tier forthis settlement currency/performance bond currency pair, by thecorresponding element in the scaled-up exchange rate down risk array forthe position.

Aggregation of position delta to the delta periods: For each combinedcommodity in the portfolio for which scanning is being performednormally (not using the “liquidation risk” scanning method), for eachposition in the combined commodity, and for each directly-calculatedrequirement level for the combined commodity: (1) Take the positiondelta. (If the position is being processed via split allocation, theposition delta will be zero and there is no need to continue.) (2) Ifthe product is processed normally, increment the period delta for thisrequirement level and for the delta period containing this contract, bythis position delta.

If the product is processed using delta-split-allocation, allocate theposition deltas out to the underlying(s) initialization of tier deltas.For intracommodity spread tiers, for each combined commodity in theportfolio, for each directly calculated requirement level, and (1) foreach intracommodity spread tier: (a) Initialize the total long delta forthe specific tier by taking the sum of all period deltas containedwithin the tier which are positive (e.g., net long.) (b) Initialize thetotal short delta for the specific tier by taking the sum of all perioddeltas contained within the tier which are negative (e.g., net short),and then by taking the absolute value of this result. (2) For theoverall tier: (a) Initialize the total long delta for the overall tierby taking the sum of the total long deltas for the specific tiers. (b)Initialize the total short delta for the overall tier by taking the sumof the total short deltas for the specific tiers.

For intercommodity spread tiers, for each combined commodity in theportfolio, for each directly calculated requirement level and (1) foreach intercommodity spread tier: (a) Initialize the total long delta forthe specific tier by taking the sum of all period deltas containedwithin the tier which are positive (e.g., net long.); (b) Initialize thetotal short delta for the specific tier by taking the sum of all perioddeltas contained within the tier which are negative (e.g., net short),and then by taking the absolute value of this result. (c) Net these tworesults against each other: subtract the total short delta from thetotal long delta. If the result is positive, store it as the total longdelta and set the total short delta to zero. If the result is negative,take its absolute value, store it as the total short delta, and set thetotal long delta to zero. (2) For the overall tier: (a) Initialize thetotal long delta for the overall tier by taking the sum of the totallong deltas for the specific tiers. (b) Initialize the total short deltafor the overall tier by taking the sum of the total short deltas for thespecific tiers. (c) Net these two results against each other: subtractthe total short delta from the total long delta. If the result ispositive, store it as the total long delta and set the total short deltato zero. If the result is negative, take its absolute value, store it asthe total short delta, and set the total long delta to zero.

Determining the Scan Risk and Related Values for Scanning AndIntercommodity Spreading Tiers:

For each combined commodity in the portfolio for which scanning is beingperformed normally (not using the “liquidation risk” scanning), For theoverall scanning tier, for the overall intercommodity spreading tier,for each specific scanning tier if there are any, and for each specificintercommodity spreading tier if there are any, and for each directlycalculated requirement level: (1) if intercurrency risk scanning wasenabled for any product family in this combined commodity: (a) for eachsettlement currency/performance bond currency pair for this combinedcommodity represented among the set of product families for whichintercurrency risk scanning was enabled: (i) compare each element in theexchange rate up array with the corresponding element in the exchangerate down array. For each element, select the larger value (morepositive or less negative), thereby yielding the overall risk array forthis tier and currency pair. (b) Sum the overall risk arrays for thevarious currency pairs for the tier, together with the array for thetier for products for which intercurrency risk scanning was not enabled(if any), thereby yielding the overall risk array for the tier.

(2) Select the largest (most positive) value in the risk array. This isthe largest loss for the tier, and the corresponding risk scenario iscalled the active scenario. For scanning tiers only, this value is alsocalled the scan risk for the tier. For intercommodity spread tiers only:(a) Select the risk array value with the same definition for pricemovement as the active scenario, but the opposite definition ofvolatility movement. This is called the paired point. (b) Take theaverage of the risk array values for the active scenario and the pairedpoint. Round this result as specified in the rounding convention fortime and volatility risks for this exchange complex, yielding anestimate of the volatility risk for the tier. (c) Take the two riskarray values with scenario definitions of (a) no price change and (b)opposite volatility changes. Take the average of these two values,yielding an estimate of the time risk for the tier. (d) Subtract theestimates of volatility risk and time risk from the scan risk, yieldingan estimate of the price risk. (e) Calculate the weighted price risk forthe tier via one of three weighted price risk calculation methods.

Determining the weighted price risk for an intercommodity spread tier:There are three methods for calculating the weighted price risk for anintercommodity spread tier: normal, normal with capping, and scanrange.If the method is normal: (1) Subtract the value of the short delta forthe tier from the value of the long delta for the tier, yielding the netdelta for the tier. (2) Divide the price risk for the tier by the netdelta. (3) Take the absolute value of this result.

If the method is scanrange: (1) Select the first non-option contractwithin the tier that has a non-zero value for its price scan range. (2)Take that price scan range. (3) Divide that value by the product of thecontract's contract scaling factor and delta-scaling factor. (This takesrelative contract size differences into account, converting the valueinto one applicable to a “standard” sized contract.)

If the method is normal with capping: (1) Calculate the weighted pricerisk first via the normal method, and again via the scanrange method.(2) Take the smaller of these two values. (In effect, it is calculatednormally, but its value is capped at the scan range.)

Determining the Scan Risk for the Combined Commodity: For each combinedcommodity within the portfolio for which scanning is being performednormally (not using the “liquidation risk” scanning method), and foreach directly calculated requirement level for that combined commodity:(1) If there are any specific scanning tiers defined for the combinedcommodity: (a) the scan risk for the combined commodity is the sum ofthe tier scan risks for each specific scanning tier. (2) But if there isonly the overall scanning tier for the combined commodity. (3) The scanrisk for the combined commodity is the scan risk for that overallscanning tier.

Determining the Scan Risk and Setting Other Values for the CombinedCommodity Using the Liquidation Risk Method

Each combined commodity for which Liquidation Risk has been specified asthe processing method for scanning will contain only physical equity ordebt securities which are considered to (a) be within the same securityfamily and (b) have the same risk level.

Each such combined commodity will have only overall tiers defined for itfor scanning, for intercommodity spreading, and for intracommodityspreading. Each such combined commodity will have precisely oneintracommodity spread defined for it, a delta-based, one to one, overalltier 1 to overall tier 1 spread. The charge rate for this spread will bespecified as a decimal fraction. Intercommodity spreads referencing thiscombined commodity will similarly reference the overall intercommodityspread tier, with a credit rate specified as a decimal fraction. Foreach combined commodity for which Liquidation Risk has been specified asthe method for determining the Scan Risk: (1) Take the sum of theLiquidation Risk Position Values for all positions for which this valueis positive. This yields the Long Liquidation Value. (2) Take the sum ofthe Liquidation Risk Position Values for all positions for which thisvalue is negative. Then take the absolute value of this sum. This yieldsthe Short Liquidation Value. (3) For each directly-calculatedrequirement level for this combined commodity: (a) Read the LiquidationRisk rates for this requirement level and combined commodity. There willbe two values, the Specific Rate and the Generic Rate. (These are alsoreferred to as the X-parameter and the Y-parameter, respectively, in theParis Bourse documentation.) (b) Take the sum of the Long LiquidationValue and the Short Liquidation Value, and multiply this result by theSpecific Rate. This yields the Specific Risk. (c) Take the absolutevalue of the difference between the Long Liquidation Value and the ShortLiquidation Value, and multiply this result by the Generic Rate. Thisyields the Generic Risk. (d) Take the sum of the Specific Risk and theGeneric Risk. (e)

Store the Long Liquidation Value as the Long Delta for the overallIntracommodity Spread Tier. (f) Store the Short Liquidation Value as theShort Delta for the overall Intracommodity Spread Tier. (g) Subtract theShort Liquidation Value from the Long Liquidation Value. If this resultis zero or positive, store it as the Long Delta for the overallIntercommodity Spread Tier. If this result is negative, take itsabsolute value and store it as the Short Delta for the overallintercommodity spread tier. (h) Set the Weighted Price Risk for theoverall intercommodity spread tier to 1.

Spreading

After determining the scan risk and the minimum commodity charge foreach combined commodity in the portfolio, the next step is to performspreading. As will be described below, the disclosed embodiments utilizethe following spreading and hybrid spreading methodologies.

Spread Groups

The SPAN algorithm supports the definition of the groups of spreads,including: Super-intercommodity spreads, Intra-commodity spreads,Pre-crossmargining spreads, Cross-margining spreads, Inter-commodityspreads, and Inter-clearing organization (“interexchange”) spreads.Intra-commodity spreads are typically used to calculate charges torecognize the risk associated with spreads formed within a combinedcommodity. The scanning process assumes perfect correlation of pricemovements among the various products grouped together within a combinedcommodity.

Inter-commodity spreads are used to recognize risk offsets, and provideappropriate credits, between positions in related combined commodities.Inter-clearing organization spreads, often referred to as interexchangespreads, are used to recognize risk offsets and provide appropriatecredits, between positions in combined commodities of different clearingorganizations or other business functions of those clearingorganizations. These are distinguished from normal intercommodityspreads in that each clearing organization involved in a particularspread is free to recognize or not recognize that spread, and to specifythe particular credit rate applicable to its own products. This may beused when a clearing organization wishes to grant a reduction to theperformance bond requirement for its own products when the risk of thoseproducts is reduced by offsetting positions on another clearingorganization, regardless of whether any formal cross-margining agreementexists between those clearing organizations, and typically in theabsence of any such agreement.

Super-intercommodity spreads are a new spread group created in order toallow the recognition of particular delta patterns across combinedcommodities, even before intracommodity spreading is performed. Forexample, this type of spread can be used to recognize a “tandem”relationship between two combined commodities (for the first combinedcommodity: long in one month, short in another; and for the secondcombined commodity: short in one month, long in another.)

Cross-margining spreads are a new group created in order to allow two ormore clearing organizations which participate in a cross-marginagreement, to define spreads which are to be evaluated before normalintra- and inter-commodity spreading is done. The newpre-cross-margining spread group gives those same clearing organizationsan opportunity to define spreads which are to be evaluated first, beforethe cross-margining spreading is done.

Spread Types

In addition to the spread group in which they are contained, spreads maybe categorized by whether they are delta-based, scanning-based, orhybrid delta-based/scanning-based. Scanning-based spreads and hybridspreads can only be used for the intercommodity spreadgroups—pre-crossmargin spreads, super-intercommodity spreads, and normalintercommodity spreads. Spreads in the groups that cross clearingorganization and/or business function boundaries—the crossmarginingspreads and the inter-clearing organization spreads—can only bedelta-based.

Delta-Based Spreading

A delta-based spread is one that is formed on a delta-basis—e.g.,according to the relative magnitudes and relationships of the remainingdelta values for each of the legs of the spread. A delta-based spreadmay contain any number of spread legs. Spreads are typically two-legged,but three, four, five or more legged-spreads may occur. Each legreferences a specific combined commodity, and for that combinedcommodity, one of: 1) an intercommodity spread tier; 2) anintracommodity spread tier, or 3) a delta period.

In addition, for each leg, a delta per spread ratio and a relativemarket side indicator are specified. The delta per spread ratio is apositive value, which indicates the amount of delta consumed for thatleg via the formation of one spread. The relative market side indicatoris either A or B, and indicates the relative relationship of theremaining deltas of the legs which must prevail in order for spreads tobe formed. For example, for a typical two-legged A to B spread, eitherthe remaining delta for the first leg must be positive and the secondleg negative, or the remaining delta for the first leg must be negativeand the second leg positive.

A delta-based spread also has defined for it a charge or creditmethod—either flat-rate, or weighted price risk. Flat-rate is typicallyused for intracommodity spreads. A charge for the spread is calculatedby taking the number of spreads formed and multiplying by the chargerate. Weighted price risk is typically used for intercommodity spreads.For each participating leg, a credit for the spread is calculated bydetermining the total number of delta consumed by the spread, times theweighted price risk (which can be thought of as the price risk perdelta), times the credit rate percentage. Accordingly, a delta-basedspread also has defined for it one or more rates, depending on how manyrequirement levels are being directly calculated.

For an intracommodity spread using the flat-rate method, the rates areconsidered to be charge rates, and a normal, positive charge rateproduces an intracommodity spread charge. A negative charge rate isallowed and would produce a negative charge—e.g., a credit.

Similarly, for an intercommodity spread using the weighted price riskmethod, a normal, positive credit rate percentage produces a positivecredit amount. If a negative credit rate had been specified for thespread, this would yield a negative credit—(e.g., a charge).

Delta-based spreads using the flat rate method may have more than onecombined commodity represented among their legs. If so, the resultingcharge is apportioned to each leg according to the relative proportionof the absolute value of its delta per spread ratio. All such combinedcommodities participating in such a spread must accordingly share thesame performance bond currency.

Spreads within Spreads

Sometimes it may be desired to use one delta-based spread to set a limiton the total number of spreads formed via a separate set of delta-basedspreads. To handle these situations generically, delta-based spreadshave been made recursive in SPAN. That is, a delta-based spread maycontain a set (one or more) of delta-based spreads, each of which maycontain a set (one or more) of delta-based spreads. There are no limitsto the numbers of levels of such recursions. The spread at the top ofsuch a hierarchy is called the top-level spread, and it is the one thatcontains the rate(s) for the spread. Spreads at lower levels do not haverates defined for them. The basic idea here is that each spread sets anupper bound on the number of spreads which can be formed by spreadscontained within it. In the typical case, there is only one level ofrecursion, with a top-level spread containing a set of child spreads,each of which does not have children. The top-level spread sets anoverall upper bound on the number of spreads formable by its childspreads.

Creating Combined Pools of Inter-Clearing Organization Spreads and ofCross-Margining Spreads

Except for spreads in the crossmargining group and the inter-clearingorganization group, spreads in each group are evaluated exchange complexby exchange complex, and it does not matter in which order the exchangecomplexes are processed. For the cross-margining group and theinter-clearing organization group, however, processing is not done byexchange complex. Instead, single pools of spreads are created whichinclude all spreads provided for any exchange complex represented in theportfolio.

Duplicate spreads may be recognized. For example, the algorithm mustrecognize that these are the same spread. Each clearing organization canonly provide a credit for its own products. In this example, whenclearing organization X specifies the spread, the credit rate(s) itspecifies only apply to its own products. And similarly for clearingorganization Y. If clearing organization X recognizes the spread whileorganization Y does not, then the credit rate specified by X will applyonly to X's products. Y's products will have a credit rate of zero. Ifboth organizations recognize the spread, there nevertheless is noguarantee that they will have the same credit rates. X may specify onerate applicable to its products, and Y may specify a different rateapplicable to its products. Also, spreads may be prioritized by greatesttotal savings. The spreads in the combined pool must be prioritizedaccording to greatest total savings across all legs.

Evaluating spreads group by group: For each exchange complex in theportfolio and for the spreads in the super-intercommodity spread group,evaluate each spread within the group in turn, in order by spreadpriority.

For each exchange complex in the portfolio and for the spreads in theintracommodity spread group, evaluate each spread within the group inturn, in order by spread priority. Finalize the spot charges for alldelta periods to which they apply.

For each exchange complex in the portfolio and for the spreads in thepre-cross-margining spread group, evaluate each spread within the groupin turn, in order by spread priority.

For the combined pool of crossmargining spreads, evaluate each spread inthe pool, ordered as described above in descending order by totalsavings.

For each exchange complex in the portfolio and for the spreads in theintercommodity spread group, evaluate each spread within the group inturn, in order by spread priority.

For the combined pool of inter-clearing organization spreads, evaluateeach spread in the pool, ordered as described above in descending orderby total savings.

Evaluating a delta-based spread—Overview: The overall process forevaluating a delta-based spread that has no child spreads includesfirst, checking to make sure that each of the spread legs is present inthe portfolio and then attempting to form spreads under each of the twopossible assumptions of market side. In other words, first attempt toform spreads assuming that the “A” legs are long and the “B” legs areshort. Then reverse the assumption and attempt to form spreads assumingthat the “A” legs are short and the “B” legs are long. Under eitherassumption, if any spreads can be formed, determine for each leg thedelta consumed by the spread. Remove the consumed delta from theremaining delta for that spread leg. Then re-evaluate delta values asneeded so that remaining period deltas, intracommodity spread tierdeltas, and intercommodity spread tier deltas are kept synchronized.Lastly, the charge or credit associated with the spreads formed isdetermined.

Determining the delta consumed for a particular leg of a delta-basedspread under a particular assumption of market side:

-   1) Take the number of spreads formed.-   2) Multiply by the delta per spread ratio for the leg.-   3) If the current assumption is that the A side is long and this is    a B leg, OR if the current assumption is that the A side is short    and this is an leg, then multiply the above result by −1 to make it    negative. (In other words, in this case, short delta has been    consumed.)

Removing the delta consumed for a particular leg of a delta-based spreadunder a particular assumption of market side:

-   1) Initialize the remaining delta to be removed, as the delta to be    consumed.-   2) If the leg references a spread tier—either an intracommodity or    an intercommodity spread tier, and either a specific tier or the    overall tier:    -   a) Beginning with the first delta period within the tier and        continuing with each subsequent delta period within the tier,        remove delta from each such period sequentially until remaining        delta to be removed is zero.-   3) But if the leg references a specific delta period, then remove    delta from that specific period.-   4) For each intracommodity or intercommodity spread tier containing    the period from which some delta was removed decrement remaining    long or short delta by the amount of delta removed from the period.

Calculating the credit for a particular leg of a delta-based spreadwhich uses the weighted price risk method, and incrementing the creditamount for the appropriate tier: This would be for a delta-based spreadthat uses the weighted price risk method. Each leg of such a spreadwould reference either an intercommodity spread tier or a delta periodfor a combined commodity. If the leg references a tier, it will beeither the overall intercommodity spread tier or, if specific tiers aredefined, a specific intercommodity spread tier.

1) Take the absolute value of the delta consumed by the spread for thisleg.2) Determine the tier to use for reading the weighted price risk:

-   -   a) If the leg references an intercommodity spread tier, select        that tier.    -   b) If the leg references a delta period:        -   i) If specific intercommodity spread tiers are defined,            select the specific tier containing this period.        -   ii) If no specific tiers are defined, select the overall            intercommodity spread tier.    -   c) Take the absolute value of the delta consumed by the spread        for this leg and this requirement level.    -   d) Multiply this result by the weighted price risk for the        selected tier and this requirement level.    -   e) Multiply this result by the credit rate for the spread for        this leg and this requirement level.    -   f) If the spread giving rise to this credit is in any spread        group other than the cross-margin spread group or the        inter-clearing organization spread group:        -   i) Increment the intercommodity spread credit for the            selected tier, by the credit for this leg for this spread.    -   g) But if the spread giving rise to this credit is in either the        cross-margin spread group or the inter-clearing organization        spread group:        -   i) Increment the inter-clearing organization spread credit            for the selected tier, by the credit for this leg for this            spread.

(As described above, if the credit rate were negative, this would yielda negative credit)

Calculating the charge for a delta-based spread which uses the flat-ratemethod: This could apply to a pre-crossmargining spread, asuper-intercommodity spread, an intracommodity spread, or anintercommodity spread. Generally (1) Take the number of spreads formed;and (2) multiply by the charge rate for the spread for this requirementlevel.

Scanning-Based Spreads

Scanning-based spreads are inherently intercommodity spreads, and canonly be present within the three spread groups which (a) include morethan one combined commodity among the legs and (b) do not cross exchangecomplexes. These groups are: pre-cross-margin, super-intercommodity, andnormal intercommodity spreads. A scanning-based spread is similar to adelta-based spread in that it contains a collection of legs. Each leg,however, references only a specific combined commodity. The relativemarket side indicator is not applicable to the legs of a scanning-basedspread. The delta per spread ratio is applicable, but, as will bedescribed below, its application is somewhat different for ascanning-based spread than for a delta-based spread.

One of the legs of a scanning-based spread is designated as the targetleg, and there is an associated parameter of the target leg called thetarget leg required flag: (1) If the target leg required flag is true,then the combined commodity designated as the target leg must be presentin the portfolio in order for the spread to be formed, and if it is not,the spread is skipped. (2) If the target leg required flag is false,then the combined commodity designated as the target leg need not bepresent in the portfolio in order for the spread to be formed.

Similarly, for each leg which is not the target (a “non-target leg”),there is a parameter called the leg-required flag. If any non-target legwhich is specified as required is not present in the portfolio, then thespread is skipped. In other words, all required non-target legs must bepresent in the portfolio in order for the spread to be formed.

As with a delta-based spread, a scanning-based spread has one or morecredit rates specified for it, for different account types andrequirement levels for those account types. All legs for ascanning-based spread must have the same scan point definitions.

Evaluating a Scanning-Based Spread: Verify that all of the required legsare represented in the portfolio. Skip the spread if not.

For the target leg, aggregate from the target leg and each of thenon-target legs, thereby yielding the new value for the target leg, eachof the eight types of position value, converted as needed to theperformance bond currency of the target leg.

For each directly calculated requirement level, For each scanning tierfor the target leg, for the target leg and for each non-target leg: (1)Perform the Risk Array Scaling and Currency Conversion Algorithm: (a)Take the risk array for the tier. (b) For each value in the risk array:(i) If this value is negative (e.g., a gain), multiply it by the creditrate expressed as a decimal fraction. (ii) If this leg is not thetarget, and if the performance bond currency for this leg is differentfrom the performance bond currency for the target leg, then convert thevalue to the performance bond currency of the target.

Take the sum all of these appropriately scaled and converted riskarrays. This yields the new risk array for the overall scanning tier forthe target leg. Select the largest loss and determine the scan risk andactive scenario, exactly as for any scanning tier.

For each non-target leg, set each value in the risk array for the tierto zero. Then repeat the process of selecting the largest loss anddetermining the scan risk, thereby setting these values to zero.

For each delta period for the target leg, for the corresponding deltaperiod for each non-target leg that exists, (1) Divide thedelta-per-spread ratio for the target leg by the delta-per-spread ratiofor this non-target leg, yielding the aggregation ratio, (2) determinethe remaining delta to be aggregated, (a) multiply the remaining deltafor this delta period by the aggregation ratio. (3) Determine theoriginal delta to be aggregated, (a) multiply the original delta forthis delta period by the aggregation ratio.

Take the sum of the remaining delta to be aggregated values from thecorresponding delta period for each non-target leg that exists, and addthis result to the remaining delta for this delta period on the targetleg, yielding the new value for remaining delta for the target leg.

Take the sum of the original delta to be aggregated values from thecorresponding delta period for each non-target leg that exists, and addthis result to the original delta for this delta period on the targetleg, yielding the new value for original delta for the target leg.

Take the sum of the Delivery (Spot) Charge for Delta Consumed by Spreadsfrom the corresponding delta period for each non-target leg that exists(converted as needed to the performance bond currency of the targetleg), and add this result to the same value on the target leg, yieldingthe new value for Delivery (Spot) Charge for Delta Consumed by Spreadsfor this delta period for the target leg.

Take the sum of the Delivery (Spot) Charge for Delta Remaining inOutrights from the corresponding delta period for each non-target legthat exists (converted as needed to the performance bond currency of thetarget leg), and add this result to the same value on the target leg,yielding the new value for Delivery (Spot) Charge for Delta Remaining inOutrights for this delta period for the target leg.

Set to zero for the corresponding delta period for each non-target leg:(1) original delta and remaining delta; (2) Delivery charge for deltaconsumed by spreads, and delivery charge for delta remaining inoutrights

For each intercommodity spread tier for the target leg:

-   1) For the target leg and for each non-target leg:    -   a) Perform the same Risk Array Scaling and Currency Conversion        Algorithm as described above for the scanning tiers-   2) Take the sum all of these appropriately scaled and converted risk    arrays. This yields the new risk array for the intercommodity spread    tier for the target leg.-   3) Aggregate from the target leg and each non-target leg, thereby    yielding the new value for the target leg, each of the following    elements:    -   a) Intercommodity spread credit (converted as needed to the        performance bond currency of the target leg)    -   b) Inter-clearing organization spread credit (converted as        needed to the performance bond currency of the target leg)-   4) Take the sum of the original delta for each delta period within    this tier which is positive, yielding the new value for original    long delta for the tier.-   5) Take the sum of the remaining delta for each delta period within    this tier which is positive, yielding the new value for remaining    long delta for the tier.-   6) Take the sum of the original delta for each delta period within    this tier which is negative, yielding the new value for original    short delta for the tier.-   7) Take the sum of the remaining delta for each delta period within    this tier which is negative, yielding the new value for remaining    short delta for the tier.-   8) Select the largest loss and determine the time risk, volatility    risk, price risk and weighted price risk, exactly as for any    intercommodity spreading tier.-   9) For each intercommodity spread tier for each non-target leg:    -   a) Set each value in the risk array for the tier to zero.    -   b) Set the original delta and remaining delta values to zero.    -   c) Set the intercommodity spread credit and inter-clearing        organization spread credit to zero.    -   d) Repeat the process of determining the largest loss,        volatility risk, time risk, price risk and weighted price risk,        thereby setting all of these values to zero.

For each intracommodity spread tier for the target leg:

-   -   1) Take the sum of the original delta for each delta period        within this tier which is positive, yielding the new value for        original long delta for the tier.    -   2) Take the sum of the remaining delta for each delta period        within this tier which is positive, yielding the new value for        remaining long delta for the tier.    -   3) Take the sum of the original delta for each delta period        within this tier which is negative, yielding the new value for        original short delta for the tier.    -   4) Take the sum of the remaining delta for each delta period        within this tier which is negative, yielding the new value for        remaining short delta for the tier.    -   5) For each intracommodity spread tier for each non-target leg:    -   a) Set the original delta and remaining delta values to zero.

For each short option minimum tier for the target leg:

-   1) Aggregate from the target leg and the equivalent tier on each    non-target leg, thereby yielding the new for the target leg, each of    the following elements:    -   a) Number of short puts    -   b) Number of short calls    -   c) Short option minimum charge (converted as needed to the        performance bond currency for the target leg)-   2) For each non-target leg:    -   a) Set the number of short puts, the number of short calls, and        the short option minimum charge, to zero.

For the target leg combined commodity for this requirement level:

-   1) Aggregate from the target leg and each non-target leg, thereby    yielding the new value for the target leg:    -   a) Intracommodity spread charge (converted as needed to the        performance bond currency of the target leg)

Hybrid Delta-Based/Scanning-Based Spreads

A hybrid delta-based/scanning-based intercommodity spread combineselements of delta-based spreading and scanning-based spreading. Hybridspreads may be present only in the normal intercommodity spread group,or the pre-crossmargining spread group. Like a regular delta-basedspread, the delta-based spread part of the hybrid spread definition willcontain a collection of delta-based spread legs. There are severalrestrictions, however, on the specification of the spread and of itsspread legs: (1) The spread is not recursive, e.g., it may not contain asubsidiary collection of delta-based spreads. (2) Each spread leg mayreference only the overall intercommodity spread tier of a specificcombined commodity. References to specific intercommodity spread tiersor to delta periods are not allowed. (3) All of the combined commoditiesreferenced as legs of the delta-based spread must have the sameperformance bond currency. (4) A charge rate must be specified for thedelta-based spread, which rate is denominated in that same performancebond currency.

Like a scanning-based spread, a hybrid spread will also specify a targetleg, which will reference a specific combined commodity. This targetcombined commodity is never one into which any products are linked. Itis not referenced by any spread until the hybrid spread for which it isspecified as the target. After this spread, it may subsequentlyparticipate in intercommodity spreading, but only as a leg of a regulardelta-based spread.

The following includes an algorithm for evaluating a hybrid spread, foreach directly-calculated requirement level:

-   1) Perform the Algorithm for evaluating a top-level delta-based    spread as described above, with one exception as specified herein:    -   a) This has the effect of determining under each assumption of        relative market-side, the number of delta-based spreads        formable, of calculating the associated charge, and of        decreasing series and tier deltas for each leg according to the        delta consumed by the spread.    -   b) The exception is that the charge calculated under each        assumption of relative market-side is not apportioned back to        the legs of the spread. Instead, the charges calculated under        each assumption are summed to yield the basis risk.-   2) Take the sum of the scan risk values for each of the overall    intercommodity spread tiers in the non-target legs participating in    the spread, yielding the total scan risk.-   3) Now perform the Algorithm for evaluating a scanning-based spread    as described above, using a 100% credit rate, but with the following    exceptions:    -   a) For each non-target leg, for the overall scanning tier, for        any specific scanning tiers, for the overall intercommodity        spreading tier, and for any specific intercommodity spreading        tiers, do not set each value in the risk array for the tier to        zero, and do not then re-evaluate for the tier the scan risk and        (for the intercommodity spread tiers) the time risk, volatility        risk, price risk and weighted price risk.    -   b) Similarly, do not aggregate from the non-target legs to the        target leg, and then set to zero on the non-target legs: the        intracommodity spread charge        -   i) for the overall intercommodity spread tier and for any            specific intercommodity spread tiers, the intercommodity            spread credit and the inter-clearing organization spread            credit        -   ii) for each delta period, the charge for delta consumed by            spreads and the charge for delta remaining in outrights        -   iii) for the overall short option minimum rate tier and for            any specific short option minimum rate tiers, the short            option minimum charge, and the number of short puts and the            number of short calls-   4) For the target leg, after determining the weighted price risk:    -   a) Save the value for the scan risk on the target leg as the        scan together risk.    -   b) For the overall intercommodity spread tier, the overall scan        tier, and any specific intercommodity spread tiers and specific        scanning tiers:        -   i) set the scan risk value to zero        -   ii) for the intercommodity spread tiers, set the time risk,            volatility risk, and price risk to zero, leaving only the            value for weighted price risk.-   5) The net result of this processing is that:    -   a) Remaining deltas have been aggregated for intracommodity        spread tiers, intercommodity spread tiers, and delta periods,        from the non-target legs to the target.    -   b) Weighted price risk has been determined for the overall        intercommodity spread tier on the target.    -   c) All other elements of the SPAN risk calculation remain with        the non-target legs: the scan risk, intracommodity spread        charge, short option minimum, spot charge, intercommodity spread        credit, and inter-clearing organization spread credit.    -   d) The value that would have been the scan risk for the target        leg in a normal scanning-based spread has been saved as the scan        together risk.-   6) Take the sum of basis risk and scan together risk. Subtract this    sum from the total scan risk. Divide this result by total scan risk.    Take the larger of this result, and zero, thereby yielding the    savings percentage.-   7) For the overall intercommodity spread tier for each non-target    leg:    -   a) Take the largest loss for the tier.    -   b) Multiply by the savings percentage, yielding the credit for        this leg for the spread.    -   c) Round this result to the normal precision for values        denominated in this currency.    -   d) Increment the intercommodity spread credit for the tier, by        this amount.    -   e) Again take the largest loss for the tier. Divide this value        by the scan together risk. Save this result as the scan risk        percentage for subsequent use.

Execution now proceeds to the next spread definition in the spreadgroup, and to the remaining spread groups to be evaluated. As it does,the overall intercommodity spread tier of the combined commodity, whichwas the target of the original hybrid spread, may participate as a legof other delta-based intercommodity spreads using the weighted pricerisk method of determining the credit.

If this occurs, the intercommodity spread credit for the original targetleg calculated as a result of that delta-based spread, is apportionedback to the original non-target legs of the original hybrid spread, inproportion to the scan risk for that leg to the total scan risk. Here'show:

For each directly-calculated requirement level for the original hybridspread target leg: (1) take the intercommodity spread credit value justcalculated. (2) For each original non-target leg for the original hybridspread: (a) Multiply the above value by the scan risk percentage forthat non-target leg. (b) Round this result to the normal precision forthe performance bond currency for that non-target leg. (c) Increment theintercommodity spread credit (or the inter-clearing organization spreadcredit if the spread now being processed is within the inter-clearingorganization spread group or the cross-margin spread group) by thisresult. (d) Set the intercommodity spread value for the original hybridspread target leg back to zero.

Finalizing the Spot Charge

This calculation will be performed for each combined commodity, afterall spreads in the intracommodity spread group have been evaluated, butbefore any of the subsequent spread groups have been processed.

For each combined commodity in the portfolio and for each directlycalculated requirement level for this combined commodity:

-   1) For each delta period for this combined commodity to which spot    charges apply:    -   a) If for this delta period it has been specified that spot        charges apply to either long or short delta, OR if it has been        specified that they apply to long delta only and the remaining        delta for the period is positive, OR if it has been specified        that they apply to short delta only and the remaining delta for        the period is negative:        -   i) Subtract the remaining delta for this period and            requirement level from the original value for delta for the            period and this requirement level. Take the absolute value            of this amount. This yields the delta consumed by spreads.        -   ii) Take the absolute value of the remaining delta for this            period. This yields the delta remaining in outrights.        -   iii) Multiply the delta consumed by spreads, by the charge            rate for delta consumed by spreads, yielding the spot charge            for delta consumed by spreads for this period and            requirement level.        -   iv) Multiply the delta remaining in outrights, by the charge            rate for delta remaining in outrights, yielding the spot            charge for delta remaining in outrights for this period and            requirement level.    -   b) Otherwise, the values for these two charges are zero.-   2) Sum the spot charge for delta consumed by spreads for each    period, yielding the total spot charge for delta consumed by spreads    for this combined commodity for this requirement level.-   3) Sum the spot charge for delta remaining in outrights for each    period, yielding the total spot charge for delta remaining in    outrights for this combined commodity for this requirement level.-   4) Sum the spot charge for delta consumed by spreads, and the spot    charge for delta remaining in outrights, yielding the total spot    charge for the combined commodity and this requirement level.

Finalizing the Intercommodity Spread Credit and the Interexchange SpreadCredit: For each combined commodity in the portfolio:

For each directly calculated requirement level for the combinedcommodity: (1) take the sum of the intercommodity spread credit for theoverall intercommodity spread tier, and the intercommodity spreadcredits for each specific intercommodity spread tier, if any. Thisyields the total intercommodity spread credit for the combinedcommodity. (2) Take the sum of the inter-clearing organization spreadcredit for the overall intercommodity spread tier, and theinter-clearing organization spread credits for each specificintercommodity spread tier, if any. This yields the total inter-clearingorganization spread credit for the combined commodity.

Finalizing the Span Requirement(s) for Directly Calculated RequirementLevels:

For each combined commodity in the portfolio, and for each directlycalculated requirement level for the combined commodity:

-   1) Take the sum of the scan risk, the intracommodity charge, and the    spot charge. (This value is sometimes called the commodity risk.)-   2) Subtract from this value, the sum of the intercommodity spread    credit and the inter-clearing organization spread credit. (This    value is sometimes called the prototype SPAN risk, or the pre-SPAN    risk.)-   3) Take the larger of this value and the short option minimum.-   4) If a risk adjustment factor is defined for this directly    calculated requirement level, multiply the above result by this risk    adjustment factor.-   5) If the positions in this combined commodity consist solely of    long positions in option products, all of which options have    non-zero values for their prices, then take the smaller of this    result and the current value of those options in the performance    bond currency.-   6) The result is the SPAN risk requirement for this requirement    level.

The third to last step is called capping the risk at long option valuefor portfolios consisting solely of long options. Note that the value atwhich the risk is capped may include both futures-style options andpremium-style options. The key factor here is not how the options arevalued, but whether they are long positions in products for which thecurrent value of the risk is limited to the current value of thepositions themselves.

Determining Derived Span Risk Requirements:

For each combined commodity represented in the portfolio, for eachdirectly calculated requirement level for this combined commodity, andfor each risk adjustment factor applicable to that requirement level orto any requirement level derived from that requirement level, processeach such risk adjustment factor in turn: (1) take the SPAN riskrequirement for the base requirement level. (2) Multiply by the riskadjustment factor, which converts a requirement from the specified baserequirement level to the specified derived requirement level. (3) If thepositions in this combined commodity consist solely of long positions inoption products, all of which options have non-zero values for theirprices, then take the smaller of this result and the current value ofthose options in the performance bond currency. (4) The result is theSPAN risk requirement for the derived requirement level.

Typically risk adjustment factors used to determine derivedrequirements, are used to determine an initial requirement level from amaintenance requirement level.

Determining the Available Net Option Value

For each combined commodity in the portfolio, determine the total netvalue in the performance bond currency of all positions in the portfoliofor this combined commodity which are valued premium-style, as follows:

-   1) Take the following four values denominated in the performance    bond currency:    -   a) value of long option positions in products valued        premium-style    -   b) value of short option positions in products valued        premium-style    -   c) value of long non-option positions in products valued        premium-style    -   d) value of short non-option positions in products valued        premium-style-   2) If there are any portion of these position values for which full    credit is not being given due the premium not yet having been paid    or collected, adjust these values accordingly to remove that    portion.-   3) Subtract the adjusted value of short option positions valued    premium-style from the adjusted value of long option positions    valued premium-style, yielding the net value of option positions    valued premium-style.-   4) Subtract the adjusted value of short non-option positions valued    premium-style from the adjusted value of long non-option positions    valued premium-style, yielding the net value of non-option positions    valued premium-style.-   5) Take the sum of these two net values, yielding the net adjusted    value of positions valued premium-style.

For each requirement level for this combined commodity (whether directlycalculated or derived): (1) If for this combined commodity capping offavailable net option value at the risk has been enabled, then take thesmaller of the net adjusted value of positions valued premium-style, andthe SPAN risk requirement, yielding the available net option value forthis requirement level. (2) But if such capping has not been enabled,the available net option value for this requirement level is equal tothe net adjusted value of positions valued premium-style.

The SPAN calculation for omnibus accounts and other gross-marginedfirm-level accounts: As described above in the introductory section,Portfolios to be margined, an omnibus account is:

-   -   a firm-level account type    -   for which total positions are maintained on a gross basis—e.g.,        they may be simultaneously long and short    -   for which subaccounts may be defined    -   for which the portion of the total long and total short        positions which are not contained in said defined subaccounts,        are considered to be the naked long and naked short positions    -   for which the naked long and naked short positions are margined        on a gross basis—in other words, treated as if each such naked        long position and each such naked short position is in a        portfolio by itself, without any risk reductions due to        offsetting positions.

Generically, a gross-margined firm-level account is any such account forwhich naked long and naked short positions are margined in this manner.An omnibus account may be considered to be an example of such an accountfor which there may also be positions in defined subaccounts.

This section describes the overall process for determining the SPAN riskrequirements and the Available Net Option Values for the combinedcommodities represented in the portfolio for gross-margined firm-levelaccounts. This process includes: 1) Determining the naked long and nakedshort positions, 2) Calculating SPAN requirements for the subaccounts,if any; 3) Calculating SPAN requirements for the naked positions; and 4)Aggregating SPAN requirements for the subaccounts with the SPANrequirements for the naked positions, in order to determine the totalSPAN requirement values for the combined commodity.

Determining the Naked Positions

For each position in the omnibus account: (1) Take the sum of allsubaccount positions in this product that are net long. (2) Subtractthis result from the Total Long position quantity for the omnibusaccount, yielding the Naked Long position. (3) Take the absolute valueof the sum of all subaccount positions in this product that are netshort. (4) Subtract this result from the Total Short position quantityfor the omnibus account, yielding the Naked Short position.

Note that for each product represented in the omnibus account portfolio,the Total Long position must be at least as great as the sum of thesubaccount positions that are net long, and the Total Short positionmust be at least as great as the absolute value of the sum of thesubaccount positions that are net short. Naked position quantities maybe zero, but by definition they may never be negative.

Calculating SPAN requirements for subaccounts: Whenever the SPANcalculation is to be performed for an omnibus account, after determiningthe naked positions, the normal SPAN calculation for net portfoliosshould be performed for each subaccount of that omnibus account, if anyare defined.

For each such subaccount, for each combined commodity represented in theportfolio for the subaccount, the result will be the SPAN riskrequirement and Available Net Option Value for each directly-calculatedand indirectly-calculated requirement level for that combined commodity.Evaluating the SPAN requirements for the subaccounts first simplifiesthe SPAN calculation for the omnibus account, in that it ensures thatthe subaccount requirements will be available for aggregation to theomnibus account when they are needed.

Calculating SPAN requirements for naked positions: For each combinedcommodity in the portfolio, for each position for this combinedcommodity, and for the naked long position quantity, perform the NakedPosition SPAN evaluation algorithm to determine for each directly andindirectly calculated requirement level for this combined commodity:

-   1) the SPAN risk requirement-   2) the Available Net Option Value-   3) For the naked short position quantity, perform the Naked Position    SPAN evaluation algorithm to determine for each directly and    indirectly calculated requirement level for this combined commodity:    -   a) the SPAN risk requirement    -   b) the Available Net Option Value-   4) For each directly and indirectly calculated requirement level for    this combined commodity:    -   a) Sum the SPAN requirement for naked longs for this requirement        level, and the SPAN requirement for naked shorts for this        requirement level, yielding the total SPAN requirement for        nakeds for this position and this requirement level.    -   b) Sum the Available Net Option Value for naked longs for this        requirement level, and the Available Net Option Value for naked        shorts for this requirement level, yielding the total Available        Net Option Value for nakeds for this position and this        requirement level.-   5) For each directly and indirectly calculated requirement level:    -   a) Take the sum of the SPAN requirement for nakeds, across all        positions for the combined commodity, yielding the SPAN        requirement for naked positions for the combined commodity for        this requirement level.    -   b) Take the sum of the Available Net Option Value for nakeds,        across all positions for the combined commodity, yielding the        Available Net Option Value for naked positions for the combined        commodity for this requirement level.

Naked Position Span Evaluation Algorithm

This algorithm is described to either the naked long quantity or thenaked short quantity of a position held in a gross-margined account,either at the firm-level or the clearing-level.

-   1) Create a net portfolio for the purpose of this calculation,    consisting solely of this naked long (or naked short) position.-   2) Apply the SPAN algorithm to this net portfolio.-   3) For each requirement level directly calculated:-   4) Determine the SPAN requirement and the Available Net Option Value    for this requirement level and for the combined commodity containing    the net position.-   5) If split allocation or margining-positions-as-equivalents caused    other combined commodities to be represented in the portfolio:-   6) For each such other combined commodity, determine the value of    the SPAN requirement and the Available Net Option Value for that    other combined commodity, in the performance bond currency of the    original combined commodity containing the position:    -   a) If the performance bond currency of this other combined        commodity is the same as the performance bond currency of the        combined commodity containing the positions, simply take the        SPAN requirement and the Available Net Option Value for that        other combined commodity.-   7) But if these two currencies are not the same:    -   a) Multiply the SPAN requirement for the other combined        commodity by the appropriate rate to convert it to the        performance bond currency of the original combined commodity,        and round this result to the normal precision for that original        performance bond currency.    -   b) Multiply the Available Net Option Value for the other        combined commodity by the same rate, and round this result to        the normal precision for that original performance bond        currency.-   8) Take the sum of these equivalent values for SPAN requirement,    across all such other combined commodities.-   9) Increment the SPAN requirement for the original combined    commodity containing the net position, by this sum.-   10) Take the sum of the equivalent values for Available Net Option    Value, across all such other combined commodities.-   11) Increment the SPAN requirement for the original combined    commodity containing the net position, by this sum.-   12) The result so far is the SPAN requirement and the Available Net    Option Value for the naked long (or naked short) position for this    directly calculated requirement level.-   13) If any requirement levels are derived from this directly    calculated requirement level, apply the risk adjustment factor(s) in    turn to determine the derived SPAN risk requirement and Available    Net Option Value for the naked long (or naked short) position for    each such derived requirement.

Aggregating SPAN requirements for Naked Positions with SPAN requirementsfor subaccounts: For each combined commodity represented in the omnibusaccount portfolio, for each requirement level for which requirementshave been determined for this portfolio, whether directly or indirectlycalculated:

-   1) Take the sum of the SPAN risk requirements for this requirement    level across all subaccount portfolios in which this combined    commodity is represented. This yields the total SPAN risk    requirement for subaccounts for this requirement level.-   2) Similarly, take the sum of the Available Net Option Values for    this requirement level across all subaccount portfolios in which    this combined commodity is represented. This yields the total    Available Net Option Value for subaccounts for this requirement    level.-   3) Take the sum of the total SPAN risk requirement for subaccounts,    and the total SPAN risk requirements for naked positions, yielding    the overall SPAN risk requirement for the combined commodity and    this requirement level.-   4) Similarly, take the sum of the total Available Net Option Value    for subaccounts, and the total Available Net Option Value for naked    positions, yielding the overall Available Net Option Value for the    combined commodity and this requirement level.

The Span Calculation for Gross-Margined Clearing-Level Accounts

When a clearing-level account is gross-margined, positions are firstmaintained on a gross basis. For any particular position in theportfolio, a Total Long position and a Total Short position are defined.Second, of the Total Long and Total Short position quantities, someportion is specified to be intercommodity spreadable and some portion issaid to be intracommodity spreadable. Positions that are neither internor intracommodity spreadable are naked. So for each position in agross-margined clearing-level portfolio, six position quantity valueswill be specified:

Total Long

Total Short

Intracommodity Spreadable Long

Intracommodity Spreadable Short

Intercommodity Spreadable Long

Intercommodity Spreadable Short

Naked Long

Naked Short

Note that the same convention as with gross-margined firm-level accountsis followed, where both long and short position quantities are expressedas positive numbers. At the CME, when clearing member firms report theirpositions for a processing cycle, they specify for each position thetotal long and short quantities, the intracommodity spreadable long andshort quantities, and the intercommodity spreadable long and shortquantities.

The naked long quantity is then determined by subtracting theintracommodity spreadable long quantity and the intercommodityspreadable long quantity from the total long quantity, and analogouslyfor the naked short quantity. By definition, the total long quantitymust always be the sum of the intracommodity spreadable long, theintercommodity spreadable long, and the naked long. The total short mustalways be the sum of the intracommodity spreadable short, theintercommodity spreadable short, and the naked short.

Overall SPAN process for gross-margined clearing-level portfolios:

For each position in the portfolio:

-   1) Determine the intracommodity spreadable net position quantity by    subtracting the intracommodity spreadable short quantity from the    intracommodity spreadable long quantity.-   2) Determine the intercommodity spreadable net position quantity by    subtracting the intercommodity spreadable short quantity from the    intercommodity spreadable long quantity.-   3) Process the portfolio of intercommodity spreadable net positions    through the SPAN algorithm as described above for net portfolios.    This yields, for each combined commodity in the portfolio, for each    directly and indirectly-calculated requirement level for that    combined commodity, the SPAN requirement and the Available Net    Option Value for the intercommodity spreadable positions.-   4) Process the portfolio of intracommodity spreadable net positions    through SPAN algorithm as described above for net portfolios, but    omit processing of all of the spread groups except the    intracommodity spread group. The result is, for each combined    commodity in the portfolio, for each directly and    indirectly-calculated requirement level for that combined commodity,    the SPAN requirement and the Available Net Option Value for the    intracommodity spreadable positions.-   5) Process each naked long and naked short position through the SPAN    algorithm for naked positions, and aggregate the resulting naked    risk requirements and available net option values to the combined    commodity level, exactly as described above for omnibus accounts.    The result is, for each combined commodity in the portfolio, for    each directly and indirectly calculated requirement level for that    combined commodity, the SPAN requirement and the Available Net    Option Value for naked positions.

For each combined commodity in the portfolio:

-   1) For each directly and indirectly calculated requirement level for    the combined commodity:-   2) Take the sum of the SPAN risk requirement for intercommodity    spreadable positions, the SPAN risk requirement for intracommodity    spreadable positions, and the SPAN risk requirement for naked    positions. The result is the total SPAN risk requirement for the    combined commodity for this requirement level.-   3) Take the sum of the Available Net Option Value for intercommodity    spreadable positions, the Available Net Option Value for    intracommodity spreadable positions, and the Available Net Option    Value for naked positions. The result is the total Available Net    Option Value for the combined commodity for this requirement level.    Aggregation of Values from Combined Commodities:

Determining values to use for aggregation for each combined commodity:

-   1) Determine the highest performance bond class for which    requirement have been calculated among all combined commodities    represented within the portfolio.-   2) For each combined commodity in the portfolio:    -   a) For each such performance bond class for which requirements        have been calculated, beginning with the core class and        ascending in priority order to the highest class represented in        the portfolio:        -   i) If requirements were calculated for this class:            -   (1) Use the calculated values for the following four                values, as the values to use for aggregation:                -   (a) SPAN requirement—maintenance—specified class                -   (b) SPAN requirement—initial—specified class                -   (c) Available Net Option Value—maintenance—specified                    class                -   (d) Available Net Option Value—initial—specified                    class                -   (e) But if requirements were not calculated for this                    class for this combined commodity:                -   (f) Use the above four values for aggregation for                    the immediately preceding class, as the values for                    aggregation for this class.

Aggregation of currency-level requirements from combined commodities toreport groups, exchange complexes, and the overall portfolio level:

1) For each exchange complex represented in the portfolio:

a) For each combined commodity report group for this exchange complex:

-   -   i) Determine the set of performance bond currencies represented        among the combined commodities for this report group within this        exchange complex.    -   ii) For each such performance bond currency represented within        the group:    -   iii) For each performance bond class for which requirements have        been calculated within the portfolio:        -   (1) Take the sum of the values for aggregation, for this            class, for any combined commodity within the group with this            performance bond currency, of the following:            -   (a) SPAN requirement—maintenance—specified class            -   (b) SPAN requirement—initial—specified class            -   (c) Available Net Option Value—maintenance—specified                class            -   (d) Available Net Option Value—initial—specified class    -   iv) The result is the specified value, for the specified class,        for the specified performance bond currency, for the specified        report group with the specified exchange complex.

For each exchange complex represented in the portfolio:

-   1) Determine the set of performance bond currencies represented    among the combined commodities within this exchange complex.-   2) For each such performance bond currency represented within the    exchange complex:-   3) For each performance bond class for which requirements have been    calculated within the portfolio:    -   a) Take the sum of the values for aggregation, for this class,        for any combined commodity within the exchange complex with this        performance bond currency, of the following:        -   (1) SPAN requirement—maintenance—specified class        -   (2) SPAN requirement—initial—specified class        -   (3) Available Net Option Value—maintenance—specified class        -   (4) Available Net Option Value—initial—specified class    -   ii) The result is the specified value, for the specified class,        for the specified performance bond currency, for the specified        exchange complex.

For the total portfolio:

-   1) Determine the set of performance bond currencies represented    among the combined commodities within the total portfolio.-   2) For each such performance bond currency represented:    -   a) For each performance bond class for which requirements have        been calculated within the portfolio:        -   i) Take the sum of the values for aggregation, for this            class, for any combined commodity within the portfolio, of            the following:            -   (1) SPAN requirement—maintenance—specified class            -   (2) SPAN requirement—initial—specified class            -   (3) Available Net Option Value—maintenance—specified                class            -   (4) Available Net Option Value—initial—specified class        -   ii) The result is the specified value, for the specified            class, for the specified performance bond currency, for the            total portfolio.

Determining Portfolio-Currency Equivalent Requirement Values

For each exchange complex within the portfolio, for each report groupwithin that exchange complex, For each performance bond class for whichrequirements have been calculated within the portfolio, and for eachperformance bond currency represented within that report group:

-   1) Determine the portfolio-currency equivalents as specified below,    of the following four values:    -   a) SPAN requirement—maintenance—specified class    -   b) SPAN requirement—initial—specified class    -   c) Available Net Option Value—maintenance—specified class    -   d) Available Net Option Value—initial—specified class    -   e) If the portfolio currency is equal to this performance bond        currency, then the portfolio currency value is the specified        value.    -   f) But if the portfolio currency is different from this        performance bond currency, determine the portfolio currency        equivalent value:        -   i) Multiply the value in the performance bond currency by            the appropriate conversion rate. Then round to the normal            precision for this portfolio currency.-   2) Take the sum of the portfolio-currency equivalent value for the    maintenance SPAN requirement for this class for the different    performance bond currencies, yielding the total portfolio-currency    equivalent value for the maintenance SPAN requirement for this class    and this report group.-   3) Take the sum of the portfolio-currency equivalent value for the    initial SPAN requirement for this class for the different    performance bond currencies, yielding the total portfolio-currency    equivalent value for the initial SPAN requirement for this class and    this report group.-   4) Take the sum of the portfolio-currency equivalent value for the    maintenance Available Net Option Value for this class for the    different performance bond currencies, yielding the total    portfolio-currency equivalent value for the maintenance Available    Net Option Value for this class and this report group.-   5) Take the sum of the portfolio-currency equivalent value for the    initial Available Net Option Value for this class for the different    performance bond currencies, yielding the total portfolio-currency    equivalent value for the initial Available Net Option Value for this    class and this report group.

For each exchange complex within the portfolio, for each performancebond class for which requirements have been calculated for this exchangecomplex within the portfolio, and for each performance bond currencyrepresented within that exchange complex:

-   1) Determine the portfolio-currency equivalents as specified below,    of the following four values, exactly as this was done above:    -   a) SPAN requirement—maintenance—specified class    -   b) SPAN requirement—initial—specified class    -   c) Available Net Option Value—maintenance—specified class    -   d) Available Net Option Value—initial—specified class-   2) Take the sum of the portfolio-currency equivalent value for the    maintenance SPAN requirement for this class for the different    performance bond currencies, yielding the total portfolio-currency    equivalent value for the maintenance SPAN requirement for this class    and this exchange complex.-   3) Take the sum of the portfolio-currency equivalent value for the    initial SPAN requirement for this class for the different    performance bond currencies, yielding the total portfolio-currency    equivalent value for the initial SPAN requirement for this class and    this exchange complex.-   4) Take the sum of the portfolio-currency equivalent value for the    maintenance Available Net Option Value for this class for the    different performance bond currencies, yielding the total    portfolio-currency equivalent value for the maintenance Available    Net Option Value for this class and this exchange complex.-   5) Take the sum of the portfolio-currency equivalent value for the    initial Available

Net Option Value for this class for the different performance bondcurrencies, yielding the total portfolio-currency equivalent value forthe initial Available Net Option Value for this class and this exchangecomplex.

For the total portfolio, for each performance bond class for whichrequirements have been calculated within the portfolio, for eachperformance bond currency represented within the total portfolio:

-   1) Determine the portfolio-currency equivalents as specified below,    of the following four values, exactly as this was done above:    -   a) SPAN requirement—maintenance—specified class    -   b) SPAN requirement—initial—specified class    -   c) Available Net Option Value—maintenance—specified class    -   d) Available Net Option Value—initial—specified class-   2) Take the sum of the portfolio-currency equivalent value for the    maintenance SPAN requirement for this class for the different    performance bond currencies, yielding the total portfolio-currency    equivalent value for the maintenance SPAN requirement for this class    and the total portfolio.-   3) Take the sum of the portfolio-currency equivalent value for the    initial SPAN requirement for this class for the different    performance bond currencies, yielding the total portfolio-currency    equivalent value for the initial SPAN requirement for this class and    the total portfolio.-   4) Take the sum of the portfolio-currency equivalent value for the    maintenance Available Net Option Value for this class for the    different performance bond currencies, yielding the total    portfolio-currency equivalent value for the maintenance Available    Net Option Value for this class and the total portfolio.-   5) Take the sum of the portfolio-currency equivalent value for the    initial Available Net Option Value for this class for the different    performance bond currencies, yielding the total portfolio-currency    equivalent value for the initial Available Net Option Value for this    class and the total portfolio.

Comparison of collateral to requirements and determination of whether anexcess or a deficiency exists: The SPAN algorithm determines the SPANrequirements and available net option value for the differentrequirement levels for each combined commodity within the portfolio, andaggregates of these values to the report group, exchange complex andtotal portfolio levels, both by performance bond currency representedand as equivalent values in the portfolio currency. The valuation ofcollateral deposited to meet requirements, the comparison of collateralto requirements and the determination of excess or deficit amounts is,strictly speaking, outside the scope of SPAN. At the clearing-level, andespecially if requirements are calculated for more than one performancebond class and if various different types of collateral are accepted,this process can be complex. For ordinary customer accounts at thefirm-level, where only one class of performance bond requirement iscalculated, the process is typically much simpler, and is describedherein:

-   1) Determine the overall value in the portfolio currency to be used    for margining (the “performance bond” value) of non-cash collateral    assets. This value is typically called the securities on deposit.-   2) Determine the net value in the portfolio currency of cash in the    account due to gains (or losses) on open positions in products    valued futures-style. This value is typically called the open trade    equity.-   3) Determine the net value in the portfolio currency of all other    cash in the account. This value is typically called the ledger    balance.-   4) Take the sum of the above three values, plus the available net    option value for the maintenance requirement for the core    performance bond class. This yields the funds available for margin    for the core maintenance requirement.-   5) Take the sum of the above three values, plus the available net    option value for the initial requirement for the core class. This    yields the funds available for margin for the core initial    requirement.-   6) Determine whether the portfolio is considered “new” or    “existing”:    -   a) If the portfolio contained no positions whatever at the close        of business for the preceding business day, then portfolio is        considered to be a new one.    -   b) Otherwise, the portfolio is considered to be a previously        existing one.-   7) If the portfolio is considered “existing” and If the funds    available for margin for the maintenance requirement for the core    class, is greater than or equal to the core maintenance SPAN    requirement:    -   a) Then the maintenance requirement is deemed to be applicable.        The applicable SPAN risk requirement is the SPAN requirement for        maintenance for the core class, and the applicable funds        available for margin is equal to the funds available for margin        for maintenance for the core class.-   8) But if the portfolio is considered “new” or if it is considered    existing, but the funds available for margin for the maintenance    requirement for the core class is less than the SPAN requirement for    maintenance for the core class:    -   a) Then the initial requirement is deemed to be applicable. The        applicable SPAN risk requirement is the SPAN requirement for        initial for the core class, and the applicable funds available        for margin is the funds available for margin for initial for the        core class.-   9) Subtract the applicable SPAN requirement from the applicable    funds available for margin, yielding the excess (if this value is    positive) or deficit (if this value is negative) amount.

Margin Offsets Across Portfolios

The SPAN process, method and system described herein has generallyrelated to calculating or determining the margin requirements withrespect to a single portfolio. However, it will be understood that thedisclosure relating to the SPAN process, method and system as well asthe margining requirements for a portfolio may be applied to multipleportfolios and more particularly to multiple portfolios backed orunderwritten by a common capital pool. For example, the teaching anddisclosure related to determining a margin for the individual contractsand positions within a single portfolio may be applied to determining anoverall or cross-portfolio margin for multiple portfolios.

Maximizing Margin Credit for Delta Neutral Portfolios

While the SPAN process herein may determine the optimal marginrequirement for a given portfolio, which includes determining any margincredits therefore, other factors may be of concern to the trader andwhich the trader may wish to balance against the optimal marginrequirement or the credit they receive therefore. Optimal margin creditmay be a credit towards a margin requirement for a given position thatmost closely approximates the maximum credit rate set by the exchange,clearing organization, or other entity, against the margin requirementfor that position.

For example, many traders utilize a trading strategy known as “deltaneutral trading” whereby the trader attempts to maintain the overalldelta of their portfolio at a neutral level by holding variousoffsetting positions. Delta is the amount by which an option's pricewill change for a corresponding change in price by the underlyingentity, e.g. the ratio of the change in price of a call option to thechange in price of the underlying stock, also referred to as a hedgeratio. Call options have positive deltas, while put options havenegative deltas. Technically, the delta is an instantaneous measure ofthe option's price change, so that the delta will be altered for evenfractional changes by the underlying entity. For futures, Delta is themeasure of the price-change relationship between an option and theunderlying futures price and is equal to the change in premium dividedby the change in futures price. A set of options is considered DeltaNeutral when they comprise positive delta options and negative deltaoptions that offset each other to produce a position which neither gainsnor decreases in value as the underlying entity (the “underlier”) movesslightly up or down. Such a position will return a profit no matterwhich way the underlying entity eventually moves as long as the move issignificant. A delta hedge is a simple type of hedge that may be widelyused by derivative traders to reduce or eliminate a portfolio's exposureto some underlier. The trader may calculate the portfolio's delta withrespect to the underlier and then may add an offsetting position in theunderlier, or another underlier, to make the portfolio's delta zero,i.e. Delta Neutral. The offsetting position may take various forms, buta spot, forward or futures position in the underlier is typical. Allthat is really required is that the position's delta substantiallyoffset that of the original portfolio. Delta hedging refers to a dynamichedging strategy using options that calls for constant adjustment of thenumber of options used, as a function of the delta of the option.

However, a portfolio that is delta neutral may not receive optimalmargin credit due to the mechanisms by which margin credits areallocated for spread positions held therein. This is because impliedmargin requirements, i.e. margin requirements which are discounted toreflect the lower risk when offsetting positions are held in the sameportfolio, are computed by offsetting the larger margin requirement ofthe two legs of the spread against only a fraction of the smaller marginrequirement of the other leg. The fraction or discount is determined bythe exchange, clearing organization, other risk management entity, orcombination thereof. As the two legs will typically have unequalquantities to maintain the delta neutral position of the portfolio, theywill have unequal margin requirements resulting in an implied creditthat deviates from the target credit offered by the exchange or clearingorganization. Ideally, the implied credit equals the target credit tobalance the interests of both the trader and the exchange/clearingorganization. However, from the trader's perspective the implied creditmay meet or exceed the target credit while from the exchange or clearingorganization's perspective, the implied credit may meet or be less thanthe target credit.

While a trader may create test portfolios and analyze them using SPAN toidentify the optimal portfolio, such manual analysis would be timeconsuming and, given the dynamic nature of the market, deliver untimelyresults. The disclosed embodiments automatically determine positions tohold which result in a delta neutral portfolio while optimizing margincredits therefore. In particular, the present embodiments determine theoptimal starting position, i.e. quantity of a given product, from whichto then determine subsequent positions, i.e. quantities of otherproducts, to remain delta neutral, while balancing this against theoptimal margin credit (where the SPAN credit amount for each position inthe portfolio most closely approximates the credit rate set by theclearing organization, across the entire portfolio). The disclosedembodiments may operate using current/real-time market data and,therefore, return timely results reflecting the current state of themarket and allowing the trader to act accordingly. In one embodiment,parallel analysis may be utilized to evaluate multiple potentialportfolios to identify the optimal portfolio, as will be discussed.

The disclosed embodiments utilize hedge ratios to determine the optimalhedge ratio and associated scanning spread. This tells traders whatratios of the quantities of products they should have in their portfolioin order to maintain the status of the portfolios as delta neutral, i.e.be delta hedged, and receive optimal margin credits therefore. Asdescribed above, a hedge ratio is the ratio, in one embodiment, of thevalue of futures contracts purchased or sold to the value of the cashcommodity being hedged, a computation necessary to minimize basis risk.The Hedge Ratio may be defined as the number of futures contractsrequired to buy or sell so as to provide the maximum offset of risk andwhich may depend on value of a futures contract, the value of theportfolio to be hedged, and the sensitivity of the movement of theportfolio price to that of the Index (Called Beta). The hedge ratio isclosely linked to the correlation between the asset (portfolio ofshares) to be hedged and underlying (index) from which Future isderived. Effectively, the best scanning based credits and the positionsneeded to get that credit are determined. While the disclosedembodiments solve for the lowest error between the implied credit and atarget credit for a given starting position and hedge ratios, as will bedescribed, the disclosed embodiments may also be used to determine thetarget credit rate.

FIG. 1 shows an exemplary risk management system 100, according to oneembodiment, for maximizing margin credits while maintaining a deltaneutral status for a portfolio. It will be appreciated that thedisclosed embodiments may be implemented in hardware, software or acombination thereof and that one or more components which are describedindividually may be combined into a single component having thedescribed functionality or they may be further divided intosub-components thereof. Further, the described operations may beperformed in parallel where one operation is not dependent upon theresults of another operation, and such parallel processing isimplementation dependent. In one embodiment, the disclosed system isintegrated with a risk management system, such as a risk managementsystem operated by an exchange, clearing organization or other entity.Alternatively, the disclosed embodiments may be offered as separateproduct or service by the exchange, clearing organization or otherentity or third party. In one embodiment, the system 100 is provided aspart of the SPAN® software published by the Chicago Mercantile ExchangeInc., located in Chicago, Ill., described above.

Herein, the phrase “coupled with” is defined to mean directly connectedto or indirectly connected through one or more intermediate components.Such intermediate components may include both hardware and softwarebased components. Further, to clarify the use in the pending claims andto hereby provide notice to the public, the phrases “at least one of<A>, <B>, . . . and <N>” or “at least one of <A>, <B>, . . . <N>, orcombinations thereof” are defined by the Applicant in the broadestsense, superseding any other implied definitions herebefore orhereinafter unless expressly asserted by the Applicant to the contrary,to mean one or more elements selected from the group comprising A, B, .. . and N, that is to say, any combination of one or more of theelements A, B, . . . or N including any one element alone or incombination with one or more of the other elements which may alsoinclude, in combination, additional elements not listed.

The exemplary risk management system 100 includes a portfolio processor102 which receives financial data 104, product specifications 108 andrisk management data 106 and, based thereon, generates a specificationof an optimal portfolio 110 as will be described. Product specification108 include specifications of the products, such as treasury futures,etc. of which user is interested in determining the optimal portfoliofor optimal margin credit while being delta hedged. The productsincluded in the product specifications 108 may be selected by thetrader, such as based on a present portfolio, or otherwise selectedbased on other criteria. In one embodiment, the products included in theproduct specification 108 may be automatically selected based onspecified criteria such as market performance, risk or applicable margincredits for the given product. Financial data 104 may include real timeor non-real time market data from a financial data source, such asBloomberg, or other source or may be provided via internal calculations,an includes hedge ratios for each of the products of interest specifiedby the product specification 108 indicating, based on market data orotherwise, the ratios of the products to hold to be delta hedged. Riskmanagement data 106 may be provided by an exchange, clearingorganization or other entity and includes real time or non-real timemargin data, such as outright margin requirements for the individualproducts of the product specification 108, and target credit rates forthe spread therebetween. In one embodiment, based on the productspecification 108, the disclosed embodiments automatically retrieve thefinancial data 104 and risk management data 106 based thereon.

FIG. 2 shows a more detailed block diagram of the system of FIG. 1 foridentifying a portfolio having both a substantially neutral delta andoptimal margin credit therefore. The portfolio processor is operative toevaluate a plurality of portfolios, each portfolio containing at leasttwo products and differing from other portfolios of the plurality ofportfolio based on the quantities of the at least two products containedtherein, the quantities of each of the at least two products specifiedto achieve a delta substantially close to neutral for the portfolio,each portfolio being further characterized by at least one spreadbetween the at least two products, each of the at least one spread beingassociated with an implied credit and a target credit. As shown in FIG.2, the portfolio processor 102 includes a test portfolio generator 202,an aggregation processor 204 and a portfolio identifier 206.

The test portfolio generator 202 creates the test portfolios 212 whichwill be tested to determine the optimal portfolio 110. Based on theproduct specification 108 and financial data 104, the test portfoliogenerator 202 creates a base portfolio 208 including the products ofinterest, labeled P_(x), and the hedge ratios therefore, labeled R_(x).Using a multiplier 210, labeled Q_(M), the test portfolio generator 202generates one or more test portfolios 212 with varying quantities of theproducts of interest by varying the quantity of one or more of theproducts of interest based on the multiplier Q_(M) and computingquantities of the remaining products based on the hedge ratios inrelation thereto. The multiplier Q_(M), as well as the starting andending values, may be varied incrementally or non-incrementally in wholenumber increments or otherwise and the variation may be defined by theuser, the exchange the clearing organization or other entity orcombination thereof, or preset or automatically defined by the system100. In one embodiment, the multiplier Q_(M) is varied in whole numberincrements starting with 1 and incrementing by 1 to a maximum of 10. Itwill be appreciated that the various test portfolios 212 may be createdand tested in parallel or serially.

For each test portfolio 212, the aggregation processor 204, which iscoupled with the test portfolio generator 202, is operative to aggregatedifferences between the implied credits and the target credits for eachspread therein. For each spread of each test portfolio, the aggregationprocessor 204 computes an implied margin requirement for the spread, anoutright margin requirement for the spread, an implied credit rate basedon the implied and outright margin requirements, and the differencebetween the implied credit and the target credit based on the impliedcredit rate and a target credit rate for the spread. As was described,the target credit rate is obtained from an exchange, clearingorganization, or combination thereof. The aggregation processor 204includes a spread identifier 214, an implied processor 216, an outrightprocessor 218, a difference processor 220 and an error accumulator 222.

The spread identifier 214 identifies each unique spread between each ofthe products of the test portfolio 212, each product being a leg of thespread. A portfolio with four products may have six unique spreadcombinations therein. The implied processor 216 is coupled with thespread identifier 214 and computes an implied margin for each spreadbased on the outright margins of each leg and the target credit rate,provided with the risk management data 106, and the quantitiesdetermined by the test portfolio generator 202 for the test portfolio212. The outright processor 218 is coupled with the spread identifier214 and computes an outright margin for each spread based on theoutright margins of each leg, provided with the risk management data106, and the quantities determined by the test portfolio generator 202for the test portfolio 212. It will be appreciated that the implied andoutright margins for each spread may be computed serially or in parallelwith each other and/or with the value for the other spreads within thetest portfolio 212 and/or the other test portfolios 212.

The difference processor 220 is coupled with the implied 216 andoutright 218 processors and computes an implied credit for each spreadbased on the difference between the implied and outright margins for thegiven spread. An error accumulator 222 is coupled with the differenceprocessor 220 and computes an error value between implied credit for thespread and the target credit rate for the spread. The differenceprocessor 220 further accumulates the error values for all of thespreads of the test portfolio 212. In one embodiment, the error betweenthe implied credit and the target credit rate is computed as a squareddifference, wherein the accumulated error for the test portfolio 212 iscomputed as a sum of the squared differences. It will be appreciatedthat other mathematical functions performing the same or similarfunction may be utilized.

It will be appreciated that more than one aggregation processor 204 maybe provided so as to be able to process more than one test portfolio 212at least substantially simultaneously.

The portfolio identifier 206 is coupled with the aggregation processorand receives the accumulated error values for each test portfolio 212.The portfolio identifier 206 is operative to identify an optimalportfolio 110 of the test portfolios 212 as the portfolio of theplurality of portfolios whose accumulated error value/aggregatedifference indicates a greater number of the at least one spread with animplied credit closest to the target credit than other portfolios of theplurality of portfolios. In one embodiment, the optimal portfolio 110 isthe test portfolio 212 identified to have the lowest accumulated errorvalue of the test portfolios 212.

FIG. 3 shows a flow chart depicting exemplary operation of the system100 of FIG. 1. In operation, a plurality of portfolios are evaluated(block 302), each portfolio containing at least two products anddiffering from other portfolios of the plurality of portfolio based onthe quantities of the at least two products contained therein, thequantities of each of the at least two products specified to achieve adelta substantially close to neutral for the portfolio, each portfoliobeing further characterized by at least one spread between the at leasttwo products, each of the at least one spread being associated with animplied credit and a target credit. For each portfolio of the pluralityof portfolios, differences between the implied credits and the targetcredits for each of the at least one spread are aggregated (block 306),such as by computing the difference between the implied credit and thetarget credit using a squared difference and summing the squareddifferences of each spread. An optimal portfolio is then identified asthe portfolio of the plurality of portfolios whose aggregate differenceindicates a greater number of the at least one spread with an impliedcredit closest to the target credit than other portfolios of theplurality of portfolios (block 310).

In one embodiment, for each of the at least one spread of each portfolioof the plurality of portfolios, an implied margin requirement for thespread is computed, an outright margin requirement for the spread iscomputed, an implied credit rate based on the implied and outrightmargin requirements is computed, and the difference between the impliedcredit and the target credit based on the implied credit rate and atarget credit rate for the spread is computed. In one embodiment, thetarget credit rate is obtained from an exchange, clearing organization,or combination thereof.

In an alternate embodiment, quantities of each of a plurality ofderivative products to include in a portfolio may be computed whereineach of the plurality of derivative products is characterized by aproduct position based on underlying product and a product deltarepresentative of a sensitivity of the product position to change inprice of the underlying product, the portfolio being characterized by aportfolio delta representative of a net sum of the product delta of eachof the plurality products included in the portfolio. The quantities arecomputed so as to optimize credit towards a margin requirement for theportfolio while maintaining the portfolio delta of the portfoliosubstantially close to zero. In operation, for at least one product ofthe plurality of products, an exemplary set of first quantities of theat least one product are identified. For each first quantity of the atleast one product of the set of first quantities: second quantities ofeach of the other of the plurality of products are computed such thatthe product delta of the second quantity of each of the other of theplurality of products substantially offsets the product delta associatedwith the first quantity of the at least one product. For each spreadcombination of the first and second quantities of the at least oneproduct and the other of the plurality of products: an implied marginfor the spread combination is computed; an outright margin for thespread combination is computed; an implied credit rate is computed forthe spread combination based on the implied margin and the outrightmargin for the spread combination; a difference is computed between theimplied credit rate and the target credit rate for the spreadcombination; and a sum is generated of each computed difference for eachspread combination of the selected quantity of the at least one product.A target quantity is then identified of the at least one product of theset of quantities having the lowest summed computed difference, thetarget quantity of the at least one product in conjunction withquantities of the other of the plurality of products, computed to offsetthe product delta associated with the target quantity of the at leastone product, representing a portfolio having optimal credit towards amargin requirement for the portfolio while maintaining the portfoliodelta of the portfolio substantially close to zero.

In one embodiment, for a single quantity of each selected product of theplurality of products, a quantity is determined of at least one otherproduct of the plurality of products such that the product delta of thequantity of the other product substantially offsets the product deltaassociated with the single quantity of the selected product. In oneembodiment, the determination is based on market data.

In one embodiment, the determination further comprises computing thequantity of the at least one other product.

In one embodiment, an outright margin requirement for each product ofthe spread combination obtained along with a target credit rate for thespread combination, such as from an exchange, a clearing organization ora combination thereof.

In one embodiment, the computing of the implied margin further includescomputing the implied margin based on the outright margin requirementfor the quantity of each product and the target credit rate and thecomputing of the outright margin further comprises computing theoutright margin based on the outright margin requirements for thequantity of each product of the spread combination.

In one embodiment, the computing of the difference between the impliedcredit rate and the target credit rate further comprises computing asquared difference, the sum being generated as a sum of the squareddifferences of each spread combination

FIG. 5 shows a table 500 of four exemplary financial products fortreasuries, 2 year treasury bond TUZ7 (denoted also as “26”), 5 yeartreasury bond FVZ7 (denoted also as “25”), 10 year treasury bond TYZ7(denoted also as “21”), and 30 year treasury bond USZ7 (denoted also as“17”). For a singular position in each of the set of financial productsof interest, a neutral equivalent position in each of the remainingfinancial products is determined, based on market data, e.g. dataprovided by Bloomberg, a proprietary calculation, or otherwise derived.Exemplary proprietary calculations for computing neutral equivalentpositions are shown in Appendix A.

The table 500 of FIG. 5 shows the ratios, referred to as hedge ratios,or equivalent neutral positions of each financial product versus theremaining financial products as derived from current market dataavailable from the Bloomberg financial data service. It will beappreciated that once a neutral relationship is determined for onecontract versus another, the inverse relationship may be derivedtherefrom, e.g. given the ratio of TUZ7 to FVZ7 of 1:1.08, the ratio ofFVZ7 to TUZ7 may computed as 1:(1/1.08) or 1:0.925926. Each valuerepresents, for a given singular position, i.e. one contract, of aparticular financial product, the off-setting position that must be heldin each of the other financial products such that the combined portfolioof the two financial products is delta neutral. Further, these hedgeratios set up a mathematical relationship which may be used, for a givenquantity of one of the financial products, to extrapolate the neutralequivalent quantities of the remaining financial products whilemaintaining the delta neutral status of the portfolio. The disclosedembodiments may be used with other financial products as well, includingderivatives other than those based on treasury securities. In oneembodiment, the products may selected from those already containedwithin a given trader's portfolio.

The disclosed embodiments compute the quantity of each of the financialproducts to include in a portfolio in order to maximize the margincredit for the portfolio, with respect to a credit rate, whilemaintaining a delta neutral status therefore. The disclosed embodimentstest variations in the quantities of the constituent financial productsto determine the optimal positions. A given financial product's quantityis set at one of a set of test quantity values and the quantities of theremaining financial products are extrapolated therefrom, as wasdescribed above, based on the hedge ratios. For example, the set of testquantity values may include incremental quantities where the incrementis 1, e.g. 1, 2, 3, 4, etc., where the increment is 0.1, e.g. 1, 1.1,1.2, 1.3, etc. or other increments. Alternatively, the set of testquantity values may include non-incremental values. Each test quantityvalue of the given financial product, along with the associatedquantities of the remaining financial products extrapolated therefrom,form a test portfolio which will be tested, as described below, todetermine the margin credit which would be allocated by a riskmanagement system, such as SPAN, and how close the determined margincredit approximates the maximum possible margin credit, based on thecredit rate, allowed by the operator of the risk management system, e.g.the exchange. As will be discussed, the test portfolio whose margincredit comes the closest to the maximum possible margin credit, i.e. hasthe least error, is determined to be the optimal portfolio having theoptimal quantities of the financial products therein.

FIG. 6 shows a table 600 which depicts an exemplary test portfolio forgiven quantity of a given financial product, e.g. 3, of the 30 yeartreasury bond, and the extrapolated quantities of the remainingfinancial products, e.g. the 2, 5 and 10 year treasury bonds, needed tomaintain the delta neutral status of the portfolio based on the hedgeratios in the table of FIG. 5. It will be appreciated that any other oneor more of the financial products could serve as the starting point fromwhich the quantities of the remaining financial products areextrapolated based on the hedge ratios. In the given example shown inFIG. 6, a quantity of 3 30 year treasury bonds is offset by 5.1510 10year treasury bonds (3*1.717), 7.8192 5 year treasury bonds (3*2.607) or8.4448 2 year treasury bonds (3*2.816).

As shown in FIG. 7, for each test portfolio, the credit-adjusted marginrequirement of each possible spread combination, referred to as the“implied margin requirement,” 702 must be compared with the maximumpossible margin requirement for that spread, referred to as the“outright margin requirement” 704 and an error or differential value isdetermined. The error values for all of the spreads of the testportfolio will be summed, as will be described below. Each financialproduct of the portfolio is spread against each of the other financialproducts, e.g. FVZ7 vs. TUZ7, TYZ7 vs. FVZ7, TYZ7 vs. TUZ7, USZ7 vs.TYZ7, USZ7 vs. FVZ7, and USZ7 vs. TUZ7, etc., each product of the spreadbeing referred to as “leg.” For an exemplary test portfolio having fourfinancial products, there will be 6 possible unique spread combinations706.

To compute the implied margin requirement 702 of a given spread 706,margin requirements 708 710 of each leg and a credit rate 712 for thespread 706 must be obtained, such as from an exchange, clearingorganization or other risk management entity (not shown). The marginrequirements 708 710 for each leg, referred to as an “outright marginrequirement,” is the margin requirement for a singular quantity of thatfinancial product alone (the total outright margin requirement being theoutright margin requirement for the product multiplied times thequantity of that product held). Therefore, the outright marginrequirement for the spread is the sum total of each leg's outrightmargin requirement 708 710 multiplied by the quantity 714 716 of thatproduct held, i.e. the quantities determined for the test portfolio. Forexample, for the test portfolio shown in FIG. 7, the outright marginrequirement 708 for the first leg (FVZ7) of the first spread (FVZ7 vs.TUZ7) is 650 and, therefore, the total outright margin for this leg is650 multiplied by 7 (the quantity 714 determined from the hedge ratios,rounded down) which equals 4550. The credit rate 712 indicates theportion, represented as a percentage, of the total outright marginrequirement that would be required if the portfolio contains both legsof the spread 706, and represents the reduction in the risk of loss whenthe two positions are held together in the same portfolio. Credit rates712 are specified or otherwise defined by the exchange, clearingorganization or other risk management entity (not shown) monitoring theportfolio risk. Exemplary credit rates 712 include 0.9, 0.8 etc.

To compute the implied margin requirement 702 of the spread 706, thelargest outright margin of the outright margins 708 710 for each leg isdetermined. The lowest outright margin of the outright margins 708 710of each leg is then determined and discounted by the credit rate 712.The implied margin requirement 702 is the difference between the largestoutright margin 708 710 of the two legs and the discounted lowestoutright margin 708 710 of the two legs. For example, for the firstspread (FVZ7 vs. TUZ7), the first leg (FVZ7) has an outright margin of4550 (650*7) and the second leg (TUZ7) has an outright margin of 5200(650*8). The largest outright margin is 5200 for the second leg, whilethe lowest outright margin is 4550 for the first leg. The credit rate is0.9 and accordingly, lowest outright margin is discounted by multiplyingit by the credit rate, or 4550*0.9 which equals 4095. The differencebetween the largest outright margin and the discounted lowest outrightmargin is then 5200−4095 or 1105.

The outright margin requirement 704 for the spread is simply the totalof the outright margin requirements 708 710 of both legs. For example,for the first spread of the test portfolio shown in FIG. 7, the impliedoutright margin requirement is 5200+4550 or 9750.

In computing the implied 702 and outright 704 margin requirements for agiven spread 706 based on the quantities 714 716 of the financialproducts determined in the test portfolio, the quantity values 714 716may be rounded up or down to the nearest whole value and, as it will beappreciated, such rounding is implementation dependent. In the exemplarytest portfolio of FIG. 7, the quantities 714 716 determined in FIG. 6based on the hedge ratios of FIG. 5, have all been rounded down to thenearest whole number.

Once the implied 702 and outright margin requirements 704 are computed,they are compared to determine the implied credit rate 718 which isindicative of the difference between the implied 702 and outright 704margin requirements. In particular, the implied margin requirement (e.g.1105) is divided by the outright margin requirement (e.g. 9750) and theresult is subtracted from 1 yielding the implied credit rate 718 whichmay be expressed as a percentage (88.67%). The implied credit rate 718is then compared with the actual credit rate 712 using squareddifference calculation to establish the error between them, i.e. theimplied credit rate is subtracted from the actual credit rate and theresult is squared yielding the error value 720 for the particular spread706. The error value 720 of each spread 706 of the test portfolio isthen summed and this total 722 will be compared with the totals fromother test portfolios.

Each test portfolio is processed and then the resultant total errorvalues 722 associated with each test portfolio are compared. The testportfolio associated with the lowest total error value 722 is theoptimal portfolio which maximizes the margin credit for the trader whilemaintaining a delta neutral status of the portfolio.

In one embodiment, the portfolio processor 102 executes on a computerhaving a Pentium-class processor, or suitable equivalent, a hard diskdrive, for example a hard disk drive having a ten (10) gigabytecapacity, a memory, for example a memory having a one (1) gigabytecapacity, and a suitable output device such as flat panel LCD display.Further, the computer executes an appropriate operating system, such asMicrosoft Windows XP, published by the Microsoft Corporation, located inRedmond, Wash. The computer system 102 further may include a networkinterface and accompanying software for coupling the system with anetwork, the interface being of a suitable type for the network, such asan Ethernet or optical based network. The network may be a public orprivate network, such as the Internet, an intranet, a virtual privatenetwork, or other TCP/IP or non-TCP/IP based network as is known.Further, secure protocols, such as sHTTP or encryption, may be includedto protect communications from being intercepted or modified and togenerally authenticate users and ensure secure operation. It will beappreciated that any suitable computer system having suitableprocessing, storage and communications capabilities may be used with thedisclosed embodiments, such as a mainframe computer, a mini-computer, aworkstation, a personal computer or a personal digital assistant. Itwill be further appreciated the disclosed embodiments may be executed ona single computer system or one or more the components may be executedon a computer system which is separate from one or more computersystem(s) executing the remaining of the components, and suitablyinterconnected, such as via a network.

While the disclosed embodiments relate to a computer software programwhich is stored in the memory of a computer and executed by theprocessor(s) of the computer to perform the disclosed functions, it willbe appreciated that one or more of the disclosed components may beimplemented in hardware or a combination of hardware and software, andis implementation dependent.

It is intended that the foregoing detailed description be regarded asillustrative rather than limiting, and that it be understood that it isthe following claims, including all equivalents, that are intended todefine the spirit and scope of this invention.

APPENDIX A Exemplary Computations of Neutral Equivalent Positions

Consider two assets Z₁ and Z₂ that follow a Wiener process. If we wouldlike to create a perfectly hedged portfolio we can do the following:Π: portfolio priceΠ: change in portfolio priceΔ: desired hedge ratio

dΠ=dZ ₁ +ΔdZ ₂

Wiener stochastic process=>

dΠ=μ _(z1) Z ₁ dt+σ _(z1) Z ₁ dW+Δ(μ_(z2) Z ₂ dt+σ _(z2) Z ₂ dW)=(μ_(z1)Z ₁+Δμ_(z2))dt+(σ_(z1) Z ₁+Δσ_(z2) Z ₂)dW

perfect hedge=>remove noise=>

(σ_(z 1)Z₁ + Δ σ_(z 2)Z₂) = 0${\text{=>}\Delta} = {{- \frac{\sigma_{z\; 1}Z_{1}}{\sigma_{z\; 2}Z_{2}}} = {- \frac{{Z_{1}}/{r_{1}}}{{Z_{2}}/{r_{2}}}}}$

where r is the underlying product (r1 for Z1 and r2 for Z2)so if Z1 is a 30 year treasury future then r1 is the 30 year spottreasury bondFor commodities (corn, wheat, soybeans) with a stable relationship overtime we can imply the hedge ration by using linear regression:let ΔZ₁ and ΔZ₂ represent the change in price of Z1 and Z2 respectivelylinear regression=>

ΔZ ₂ =α+βΔZ ₁+ε

=>β is desired perfect hedge ratio

$\beta = {\frac{{cov}\left( {{\Delta \; Z_{2}},{\Delta \; Z_{1}}} \right)}{{var}\left( {\Delta \; Z_{2}} \right)} = {{{corr}\left( {{\Delta \; Z_{2}},{\Delta \; Z_{1}}} \right)}*\frac{\sigma_{z\; 1}}{\sigma_{z\; 2}}}}$

wherecov: covariancevar: variancecorr: correlation

1. A computer implemented method of computing quantities of each of aplurality of derivative products to include in a portfolio, each of theplurality of derivative products being characterized by a productposition based on underlying product and a product delta representativeof a sensitivity of the product position to change in price of theunderlying product, the portfolio being characterized by a portfoliodelta representative of a net sum of the product delta of each of theplurality products included in the portfolio, the quantities beingcomputed so as to optimize credit towards a margin requirement for theportfolio while maintaining the portfolio delta of the portfoliosubstantially close to zero, the computer including a processor, themethod comprising: for at least one product of the plurality ofproducts, identifying, by the processor, an exemplary set of firstquantities of the at least one product and for each first quantity ofthe at least one product of the set of first quantities: computing, bythe processor, second quantities of each of the other of the pluralityof products such that the product delta of the second quantity of eachof the other of the plurality of products substantially offsets theproduct delta associated with the first quantity of the at least oneproduct; and for each spread combination of the first and secondquantities of the at least one product and the other of the plurality ofproducts: computing, by the processor, an implied margin for the spreadcombination; computing, by the processor, an outright margin for thespread combination; computing, by the processor, an implied credit ratefor the spread combination based on the implied margin and the outrightmargin for the spread combination; computing, by the processor, adifference between the implied credit rate and the target credit ratefor the spread combination; generating, by the processor, a sum of eachcomputed difference for each spread combination of the selected quantityof the at least one product; and wherein the method further includes:identifying, by the processor, a target quantity of the at least oneproduct of the set of quantities having the lowest summed computeddifference, the target quantity of the at least one product inconjunction with quantities of the other of the plurality of products,computed to offset the product delta associated with the target quantityof the at least one product, representing a portfolio having optimalcredit towards a margin requirement for the portfolio while maintainingthe portfolio delta of the portfolio substantially close to zero.
 2. Thecomputer implemented method of claim 1 further comprising: for a singlequantity of each selected product of the plurality of products,determining, by the processor, a quantity of at least one other productof the plurality of products such that the product delta of the quantityof the other product substantially offsets the product delta associatedwith the single quantity of the selected product.
 3. The computerimplemented method of claim 2 wherein the determining is based on marketdata.
 4. The computer implemented method of claim 2 wherein thedetermining further comprises computing, by the processor, the quantityof the at least one other product.
 5. The computer implemented method ofclaim 1 further comprising: obtaining, by the processor, an outrightmargin requirement for each product of the spread combination; andobtaining, by the processor, a target credit rate for the spreadcombination.
 6. The computer implemented method of claim 5 wherein theoutright margin requirements and the target rate are obtained from anexchange, a clearing organization or a combination thereof.
 7. Thecomputer implemented method of claim 5 wherein the computing of theimplied margin further comprises computing, by the processor, theimplied margin based on the outright margin requirement for the quantityof each product and the target credit rate;
 8. The computer implementedmethod of claim 1 wherein the computing of the outright margin furthercomprises computing, by the processor, the outright margin based on theoutright margin requirements for the quantity of each product of thespread combination.
 9. The computer implemented method of claim 1wherein the computing of the difference between the implied credit rateand the target credit rate further comprises computing, by theprocessor, a squared difference, the sum being generated as a sum of thesquared differences of each spread combination.
 10. A system forcomputing quantities of each of a plurality of derivative products toinclude in a portfolio, each of the plurality of derivative productsbeing characterized by a product position based on underlying productand a product delta representative of a sensitivity of the productposition to change in price of the underlying product, the portfoliobeing characterized by a portfolio delta representative of a net sum ofthe product delta of each of the plurality products included in theportfolio, the quantities being computed so as to optimize credittowards a margin requirement for the portfolio while maintaining theportfolio delta of the portfolio substantially close to zero, the systemcomprising: a portfolio processor operative to, for at least one productof the plurality of products, identify an exemplary set of firstquantities of the at least one product and for each first quantity ofthe at least one product of the set of first quantities: compute secondquantities of each of the other of the plurality of products such thatthe product delta of the second quantity of each of the other of theplurality of products substantially offsets the product delta associatedwith the first quantity of the at least one product; and for each spreadcombination of the first and second quantities of the at least oneproduct and the other of the plurality of products: compute an impliedmargin for the spread combination; compute an outright margin for thespread combination; compute an implied credit rate for the spreadcombination based on the implied margin and the outright margin for thespread combination; compute a difference between the implied credit rateand the target credit rate for the spread combination; generate a sum ofeach computed difference for each spread combination of the selectedquantity of the at least one product; and wherein the portfolioprocessor is further operative to identify a target quantity of the atleast one product of the set of quantities having the lowest summedcomputed difference, the target quantity of the at least one product inconjunction with quantities of the other of the plurality of products,computed to offset the product delta associated with the target quantityof the at least one product, representing a portfolio having optimalcredit towards a margin requirement for the portfolio while maintainingthe portfolio delta of the portfolio substantially close to zero. 11.The system of claim 10 wherein the portfolio processor is furtheroperative to, for a single quantity of each selected product of theplurality of products, determine a quantity of at least one otherproduct of the plurality of products such that the product delta of thequantity of the other product substantially offsets the product deltaassociated with the single quantity of the selected product.
 12. Thesystem of claim 11 wherein the determination is based on market data.13. The system of claim 11 wherein the portfolio processor is furtheroperative to compute the quantity of the at least one other product. 14.The system of claim 10 the portfolio processor is further operative toobtain an outright margin requirement for each product of the spreadcombination and obtain a target credit rate for the spread combination.15. The system of claim 14 wherein the outright margin requirements andthe target rate are obtained from an exchange, a clearing organizationor a combination thereof.
 16. The system of claim 14 wherein theportfolio processor is further operative to compute the implied marginbased on the outright margin requirement for the quantity of eachproduct and the target credit rate;
 17. The system of claim 10 whereinthe portfolio processor is further operative to compute the outrightmargin based on the outright margin requirements for the quantity ofeach product of the spread combination.
 18. The system of claim 10wherein the portfolio processor is further operative to, to computer thedifference between the implied credit rate and the target credit rate,compute a squared difference, the sum being generated as a sum of thesquared differences of each spread combination.
 19. A system forcomputing quantities of each of a plurality of derivative products toinclude in a portfolio, each of the plurality of derivative productsbeing characterized by a product position based on underlying productand a product delta representative of a sensitivity of the productposition to change in price of the underlying product, the portfoliobeing characterized by a portfolio delta representative of a net sum ofthe product delta of each of the plurality products included in theportfolio, the quantities being computed so as to optimize credittowards a margin requirement for the portfolio while maintaining theportfolio delta of the portfolio substantially close to zero, the systemcomprising: for at least one product of the plurality of products, meansfor identifying an exemplary set of first quantities of the at least oneproduct and for each first quantity of the at least one product of theset of first quantities: means for computing second quantities of eachof the other of the plurality of products such that the product delta ofthe second quantity of each of the other of the plurality of productssubstantially offsets the product delta associated with the firstquantity of the at least one product; and for each spread combination ofthe first and second quantities of the at least one product and theother of the plurality of products: means for computing an impliedmargin for the spread combination; means for computing an outrightmargin for the spread combination; means for computing an implied creditrate for the spread combination based on the implied margin and theoutright margin for the spread combination; means for computing adifference between the implied credit rate and the target credit ratefor the spread combination; means for generating a sum of each computeddifference for each spread combination of the selected quantity of theat least one product; and wherein the system further includes: means foridentifying a target quantity of the at least one product of the set ofquantities having the lowest summed computed difference, the targetquantity of the at least one product in conjunction with quantities ofthe other of the plurality of products, computed to offset the productdelta associated with the target quantity of the at least one product,representing a portfolio having optimal credit towards a marginrequirement for the portfolio while maintaining the portfolio delta ofthe portfolio substantially close to zero.